Integration Formulas

Integration Formulas 

In this post, you will get all the formulas required to solve integration problems.

1] Integration of Standard Function 

Here formulas of Integration of Standard Functions are given-

1]  ∫ dx= x+c

2]  ∫ 1/x = logx+c

3]  ∫ dx = e^x +c

4]  ∫ a^x dx = a^x/loga +c

5]  ∫ cosx dx = sinx+c

6]  ∫ sinx dx = -cosx+c

7]  ∫ sec²x dx = tanx+c

8]  ∫ cosec²x dx = -cotx+c

9]  ∫ secx.tanx dx = secx+c

10] ∫ cosecx.cotx dx = -cosecx+c

11] ∫ 1/√(1- x²) dx = Sin^-1x+c

12] ∫ -1/√(1- x²) dx = -Cos^-1x+c

13] ∫ 1/(1+x²) dx =  tan^-1x+c

14] ∫ 1/(1+x²) dx =  cot^-1x+c 

15]  ∫ 1/x√( x²-1) dx = sec^-1x+c

16] ∫ 1/x√( x²-1) dx  = -cosec^-1x+c

17] ∫ cosecx dx = log (cosecx-cotx)

18] ∫ 1/√(x²+a²) dx = log |x+ √(x²+a²)| +c

19] ∫ 1/√(x²-a²) dx = log |x+ √(x²-a²)| +c

20] ∫ √(x²+a²) dx = x/2 √x²+a²  + a² /2 log(x+ √x²+a²)+c

21] ∫ √(x²-a²) dx =  x/2 √x²-a²  - a² /2 log(x+ √x²-a²)+c

22]  ∫ 1/√a²-x² dx =  Sin^-1(x/a) +c

23]  ∫ √a²-x² dx =  x/2 √a²-x²  + a² /2 Sin^-1(x/a) +c

24] ∫ 1/√a²+x² dx =  1/a tan^-1(x/a) 

2] Integration of Composite Function

Below are some formula of composite function for integration

3] Some Standard Formula

Below are some Standard formula  for integration

4] Some Substitution Formula

Below are some Substitution formula  for integration

This were the some basic formulas of Integration

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