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 +^@#16:
 +!جدول انتگرال توابع گویا
 @@{TEX()} {\int dx=x+C} {TEX}@@ @@{TEX()} {\int dx=x+C} {TEX}@@
 @@{TEX()} {\int x^n dx=\frac{x^{n+1}}{n+1}+C \qquad (n\neq -1)} {TEX}@@ @@{TEX()} {\int x^n dx=\frac{x^{n+1}}{n+1}+C \qquad (n\neq -1)} {TEX}@@
 @@{TEX()} {\int \frac{1}{x}dx=ln |x|+C} {TEX}@@ @@{TEX()} {\int \frac{1}{x}dx=ln |x|+C} {TEX}@@
 @@{TEX()} {\int \frac{dx}{a^2+x^2}=\frac{1}{a}arctan \frac{x}{a} +C} {TEX}@@ @@{TEX()} {\int \frac{dx}{a^2+x^2}=\frac{1}{a}arctan \frac{x}{a} +C} {TEX}@@
 +---
 @@{TEX()} {\int (ax+b)^n dx=\frac{(ax+b)^{n+1}}{a(n+1)} \qquad (n\neq -1)} {TEX}@@ @@{TEX()} {\int (ax+b)^n dx=\frac{(ax+b)^{n+1}}{a(n+1)} \qquad (n\neq -1)} {TEX}@@
 @@{TEX()} {\int \frac{dx}{ax+b}=\frac{1}{a} ln|ax+b|} {TEX}@@ @@{TEX()} {\int \frac{dx}{ax+b}=\frac{1}{a} ln|ax+b|} {TEX}@@
 @@{TEX()} {\int x(ax+b)^ndx=\frac{a(n+1)x-b}{a^2(n+1)(n+2)}(ax+b)^{n+1} \qquad (n\notin \{-1,-2 \})} {TEX}@@ @@{TEX()} {\int x(ax+b)^ndx=\frac{a(n+1)x-b}{a^2(n+1)(n+2)}(ax+b)^{n+1} \qquad (n\notin \{-1,-2 \})} {TEX}@@
 @@{TEX()} {\int \frac{xdx}{ax+b}=\frac{x}{a}-\frac{b}{a^2} ln|ax+b|} {TEX}@@ @@{TEX()} {\int \frac{xdx}{ax+b}=\frac{x}{a}-\frac{b}{a^2} ln|ax+b|} {TEX}@@
 @@{TEX()} {\int \frac{xdx}{(ax+b)^2}=\frac{b}{a^2(ax+b)}+\frac{1}{a^2}ln|ax+b|} {TEX}@@ @@{TEX()} {\int \frac{xdx}{(ax+b)^2}=\frac{b}{a^2(ax+b)}+\frac{1}{a^2}ln|ax+b|} {TEX}@@
 @@{TEX()} {\int \frac{xdx}{(ax+b)^n}=\frac{a(1-n)x-b}{a^2(n-1)(n-2)(ax+b)^{n-1}} \qquad n\notin \{1,2\}} {TEX}@@ @@{TEX()} {\int \frac{xdx}{(ax+b)^n}=\frac{a(1-n)x-b}{a^2(n-1)(n-2)(ax+b)^{n-1}} \qquad n\notin \{1,2\}} {TEX}@@
 @@{TEX()} {\int \frac{x^2dx}{ax+b}=\frac{1}{a^3}\Bigg( \frac{(ax+b)^2}{2}-2b(ax+b)+b^2ln|ax+b| \Bigg)} {TEX}@@ @@{TEX()} {\int \frac{x^2dx}{ax+b}=\frac{1}{a^3}\Bigg( \frac{(ax+b)^2}{2}-2b(ax+b)+b^2ln|ax+b| \Bigg)} {TEX}@@
 @@{TEX()} {\int \frac{x^2dx}{(ax+b)^2}=\frac{1}{a^3}\Bigg( ax+b-2bln|ax+b|-\frac{b^2}{ax+b} \Bigg)} {TEX}@@ @@{TEX()} {\int \frac{x^2dx}{(ax+b)^2}=\frac{1}{a^3}\Bigg( ax+b-2bln|ax+b|-\frac{b^2}{ax+b} \Bigg)} {TEX}@@
 @@{TEX()} {\int \frac{x^2dx}{(ax+b)^3}=\frac{1}{a^3} \Bigg(ln|ax+b|+\frac{2b}{ax+b}-\frac{b^2}{2(ax+b)^2} \Bigg)} {TEX}@@ @@{TEX()} {\int \frac{x^2dx}{(ax+b)^3}=\frac{1}{a^3} \Bigg(ln|ax+b|+\frac{2b}{ax+b}-\frac{b^2}{2(ax+b)^2} \Bigg)} {TEX}@@
 @@{TEX()} {\int \frac{x^2dx}{(ax+b)^n}=\frac{1}{a^3} \Bigg( -\frac{(ax+b)^{3-n}}{(n-3)}+\frac{2b(a+b)^{2-n}}{(n-2)}-\frac{b^2(ax+b)^{1-n}}{(n-1)} \Bigg) \qquad n\notin \{1,2,3\}} {TEX}@@ @@{TEX()} {\int \frac{x^2dx}{(ax+b)^n}=\frac{1}{a^3} \Bigg( -\frac{(ax+b)^{3-n}}{(n-3)}+\frac{2b(a+b)^{2-n}}{(n-2)}-\frac{b^2(ax+b)^{1-n}}{(n-1)} \Bigg) \qquad n\notin \{1,2,3\}} {TEX}@@
 @@{TEX()} {\int \frac{dx}{x(ax+b)}=-\frac{1}{b}ln \Bigg|\frac{ax+b}{x} \Bigg|} {TEX}@@ @@{TEX()} {\int \frac{dx}{x(ax+b)}=-\frac{1}{b}ln \Bigg|\frac{ax+b}{x} \Bigg|} {TEX}@@
 @@{TEX()} {\int \frac{dx}{x^2(ax+b)^2}=-a \Bigg( \frac{1}{b^2(ax+b)}+\frac{1}{ab^2x}-\frac{2}{b^3}ln \Bigg|\frac{ax+b}{x} \Bigg| \Bigg)} {TEX}@@ @@{TEX()} {\int \frac{dx}{x^2(ax+b)^2}=-a \Bigg( \frac{1}{b^2(ax+b)}+\frac{1}{ab^2x}-\frac{2}{b^3}ln \Bigg|\frac{ax+b}{x} \Bigg| \Bigg)} {TEX}@@
 @@{TEX()} {\frac{dx}{x^2+a^2}=\frac{1}{a} arctan \frac{x}{a}} {TEX}@@ @@{TEX()} {\frac{dx}{x^2+a^2}=\frac{1}{a} arctan \frac{x}{a}} {TEX}@@
 @@{TEX()} {\int \frac{dx}{x^2-a^2}=-\frac{1}{a} arctanh \frac{x}{a}=\frac{1}{2a}ln \frac{a-x}{a+x} \qquad (|x|<|a|)} {TEX}@@ @@{TEX()} {\int \frac{dx}{x^2-a^2}=-\frac{1}{a} arctanh \frac{x}{a}=\frac{1}{2a}ln \frac{a-x}{a+x} \qquad (|x|<|a|)} {TEX}@@
 @@{TEX()} {\int \frac{dx}{x^2-a^2}=-\frac{1}{a} arccoth \frac{x}{a}=\frac{1}{2a}ln \frac{x-a}{x+a} \qquad (|x|>|a|)} {TEX}@@ @@{TEX()} {\int \frac{dx}{x^2-a^2}=-\frac{1}{a} arccoth \frac{x}{a}=\frac{1}{2a}ln \frac{x-a}{x+a} \qquad (|x|>|a|)} {TEX}@@
 @@{TEX()} {\int \frac{dx}{ax^2+bx+c}=\frac{2}{\sqrt{4ac-b^2}} arctan \frac{2ax+b}{\sqrt{4ac-b^2} \qquad (4ac-b^2>0)}} {TEX}@@ @@{TEX()} {\int \frac{dx}{ax^2+bx+c}=\frac{2}{\sqrt{4ac-b^2}} arctan \frac{2ax+b}{\sqrt{4ac-b^2} \qquad (4ac-b^2>0)}} {TEX}@@
 @@{TEX()} {\int \frac{dx}{ax^2+bx+c}=\frac{2}{\sqrt{b^2-4ac}}arctanh \frac{2ax+b}{\sqrt{b^2-4ac}}=\frac{1}{\sqrt{b^2-4ac}}ln \Bigg| \frac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}} \Bigg| \qquad 4ac-b^2<0} {TEX}@@ @@{TEX()} {\int \frac{dx}{ax^2+bx+c}=\frac{2}{\sqrt{b^2-4ac}}arctanh \frac{2ax+b}{\sqrt{b^2-4ac}}=\frac{1}{\sqrt{b^2-4ac}}ln \Bigg| \frac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}} \Bigg| \qquad 4ac-b^2<0} {TEX}@@
 @@{TEX()} {\int \frac{dx}{ax^2+bx+c}=-\frac{2}{2ax+b} \qquad (4ac-b^2=0)} {TEX}@@ @@{TEX()} {\int \frac{dx}{ax^2+bx+c}=-\frac{2}{2ax+b} \qquad (4ac-b^2=0)} {TEX}@@
 @@{TEX()} {\int \frac{xdx}{ax^2+bx+c}=\frac{1}{2a}ln \big|ax^2 +bx+c \big|-\frac{b}{2a}\int \frac{dx}{ax^2+bx+c}} {TEX}@@ @@{TEX()} {\int \frac{xdx}{ax^2+bx+c}=\frac{1}{2a}ln \big|ax^2 +bx+c \big|-\frac{b}{2a}\int \frac{dx}{ax^2+bx+c}} {TEX}@@
 @@{TEX()} {\int\frac{(mx+n)dx}{ax^2+bx+c}=\frac{m}{2a}ln \big|ax^2+bx+c \big| +\frac{2an - bm}{a \sqrt{4ac-b^2}} arctan \frac{2ax+b}{\sqrt{4ac-b^2}} \qquad (4ac-b^2>0)} {TEX}@@ @@{TEX()} {\int\frac{(mx+n)dx}{ax^2+bx+c}=\frac{m}{2a}ln \big|ax^2+bx+c \big| +\frac{2an - bm}{a \sqrt{4ac-b^2}} arctan \frac{2ax+b}{\sqrt{4ac-b^2}} \qquad (4ac-b^2>0)} {TEX}@@
 @@{TEX()} {\int\frac{(mx+n)dx}{ax^2+bx+c}=\frac{m}{2a}ln \big|ax^2+bx+c \big| +\frac{2an - bm}{a \sqrt{b^2-4ac}} arctanh \frac{2ax+b}{\sqrt{b^2-4ac}} \qquad (4ac-b^2<0)} {TEX}@@ @@{TEX()} {\int\frac{(mx+n)dx}{ax^2+bx+c}=\frac{m}{2a}ln \big|ax^2+bx+c \big| +\frac{2an - bm}{a \sqrt{b^2-4ac}} arctanh \frac{2ax+b}{\sqrt{b^2-4ac}} \qquad (4ac-b^2<0)} {TEX}@@
 @@{TEX()} {\int\frac{(mx+n)dx}{ax^2+bx+c}=\frac{m}{2a}ln \big|ax^2+bx+c \big| -\frac{2an - bm}{a (2ax+b)} \qquad (4ac-b^2=0)}} {TEX}@@ @@{TEX()} {\int\frac{(mx+n)dx}{ax^2+bx+c}=\frac{m}{2a}ln \big|ax^2+bx+c \big| -\frac{2an - bm}{a (2ax+b)} \qquad (4ac-b^2=0)}} {TEX}@@
 @@{TEX()} {\int \frac{dx}{(ax^2+bx+c)^n}=\frac{2ax+b}{(n-1)(4ac-b^2)(ax^2+bx+c)^{n-1}}+\frac{(2n-3)2a}{(n-1)(4ac-b^2)}\int \frac{dx}{(ax^2+bx+c)^{n-1}}} {TEX}@@ @@{TEX()} {\int \frac{dx}{(ax^2+bx+c)^n}=\frac{2ax+b}{(n-1)(4ac-b^2)(ax^2+bx+c)^{n-1}}+\frac{(2n-3)2a}{(n-1)(4ac-b^2)}\int \frac{dx}{(ax^2+bx+c)^{n-1}}} {TEX}@@
 @@{TEX()} {\int \frac{xdx}{(ax^2+bx+c)^n}=\frac{bx+2c}{(n-1)(4ac-b^2)(ax^2+bx+c)^{n-1}}-\frac{b(2n-3)}{(n-1)(4ac-b^2)}\int \frac{dx}{(ax^2+bx+c)^{n-1}}} {TEX}@@ @@{TEX()} {\int \frac{xdx}{(ax^2+bx+c)^n}=\frac{bx+2c}{(n-1)(4ac-b^2)(ax^2+bx+c)^{n-1}}-\frac{b(2n-3)}{(n-1)(4ac-b^2)}\int \frac{dx}{(ax^2+bx+c)^{n-1}}} {TEX}@@
 @@{TEX()} {\int \frac{dx}{x(ax^2+bx+c)}=\frac{1}{2c} ln \Bigg|\frac{x^2}{ax^2+bx+c}\Bigg|-\frac{b}{2c}\int \frac{dx}{ax^2+bx+c}} {TEX}@@ @@{TEX()} {\int \frac{dx}{x(ax^2+bx+c)}=\frac{1}{2c} ln \Bigg|\frac{x^2}{ax^2+bx+c}\Bigg|-\frac{b}{2c}\int \frac{dx}{ax^2+bx+c}} {TEX}@@
-
+---
!همچنین ببینید:
*((جدول انتگرال توابع گنگ))
*((جدول انتگرال توابع لگاریتمی))
*((جدول انتگرال توابع نمایی))
*((جدول انتگرال توابع مثلثاتی))
*((جدول انتگرال معکوس توابع مثلثاتی))
*((جدول انتگرال توابع هیپربولیک))
#@^

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 یکشنبه 15 مرداد 1385 [12:23 ]   2   سعید صدری      v  c  d  s 
 پنج شنبه 12 مرداد 1385 [09:16 ]   1   سعید صدری      v  c  d  s 


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