Table of Integrals - Useful referance

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1 - Integrals of Elementary Functions.

1.1   ò dx = x + c

1.2   ò k dx = k x + c , where k is a constant.

1.3   ò xⁿ dx = x^{n + 1} / (n + 1) + c

1.4   ò (1 / x) dx = ln |x| + c

2 - Integrals of Elementary Trigonometric Functions : sin x, cos x, tan x, cot x, sec x and csc x.

3 - Integrals Involving More Than One Trigonometric Function.

3.1   ò sec x tan x dx = sec x + c

3.2   ò csc x cot x dx = -csc x + c

3.3   ò sin mx sin nx dx =

-sin [(m + n)x] / 2(m + n) + sin [(m - n)x] / 2(m - n) + c

with m not equal to n.

3.4   ò cos mx cos nx dx =

sin [(m + n)x] / 2(m + n) + sin [(m - n)x] / 2(m - n) + c

with m not equal to n.

3.5   ò sin mx cos nx dx =

-cos [(m + n)x] / 2(m + n) - cos [(m - n)x] / 2(m - n) + c

with m not equal to n.

4 - Integrals Involving Exponential and Logarithmic Functions.

4.1   ò e^x dx = e^x + c

4.2   ò a^x dx = a^x / ln a + c

4.3   ò ln x dx = x ln x - x + c

5 - Integrals of Inverse Trigonometric functions: arcsin x, arccos x, arctan x, arccot x, arcsec x and arccsc x.

5.1   ò arcsin x dx = x arcsin x + sqrt (1 - x²) + c

5.2   ò arccos x dx = x arccos x - sqrt (1 - x²) + c

5.3   ò arctan x dx = x arctan x - ln [sqrt (1 + x²)] + c

5.4   ò arccot x dx = x arccot x + ln sqrt (1 + x²) + c

5.5   ò arcsec x dx = x arcsec x - ln [x + sqrt (x² - 1)] + c

5.6   ò arccsc x dx = x arccsc x + ln [x + sqrt (x² - 1)] + c

6 - Integrals Involving Exponential and Sine and Cosine Functions.

6.1 òe^ax sin bx dx = (e^ax / (a² + b²) (a*sin bx - b*cos bx) + c

6.2 òe^ax cos bx dx = (e^ax / (a² + b²) (b*sin bx + a*cos bx) + c

7 - Integrals Involving Hyperbolic Functions: sinh x, cosh x, tanh x, coth x, sech x, csch x.

7.1   ò sinh x dx = cosh x + c

7.2   ò cosh x dx = sinh x + c

7.3   ò sech x tanh x dx = -sech x + c

7.4   ò csch x coth x dx = -csch x + c

7.5   ò sech² x dx = tanh x + c

7.6   ò csch² x dx = -coth x + c

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