Integration by Some Particular Function
Advanced Integration Formulas
∫1/(x
2
- a
2
).dx = 1/2a.log|(x - a)(x + a| + C
∫ 1/(a
2
- x
2
).dx =1/2a.log|(a + x)(a - x)| + C
∫1/(x
2
+ a
2
).dx = 1/a.tan
-1
x/a + C
∫1/√(x
2
- a
2
)dx = log|x +√(x
2
- a
2
)| + C
∫ √(x
2
- a
2
).dx =1/2.x.√(x
2
- a
2
)-a
2
/2 log|x + √(x
2
- a
2
)| + C
∫1/√(a
2
- x
2
).dx = sin
-1
x/a + C
∫√(a
2
- x
2
).dx = 1/2.x.√(a
2
- x
2
).dx + a
2
/2.sin-1 x/a + C
∫1/√(x
2
+ a
2
).dx = log|x + √(x
2
+ a
2
)| + C
∫ √(x
2
+ a
2
).dx =1/2.x.√(x
2
+ a
2
)+ a
2
/2 . log|x + √(x
2
+ a
2
)| + C
Information: Integration by Some Particular Function