Integrate the following with respect to x : absin2xa2+b2sin2x

Integrate the following with respect to x :

`(sin 2x)/("a"^2 + "b"^2 sin^2x)`

Sum

`int (sin 2x)/("a"^2 + "b"^2 sin^2x) "d"x`

Put a² + b² sin²x = u

(0 + b² × 2 sin x cos x) dx = du

b² sin 2x dx = du

sin 2x dx = `1/"b"^2 "du"`

`int (sin 2x)/("a"^2 + "b"^2 sin^2x) "d"x = int (1/"b"^2 "du")/"u"`

= `1/"b"^2 log|"u"| + "c"`

`int (sin 2x)/("a"^2 + "b"^2 sin^2x) "d"x = 1/"b"^2 log|"a"^2 + "b"^2 sin^2 x| + "c"`

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Chapter 11: Integral Calculus - Exercise 11.6 [Page 206]

Chapter 11 Integral Calculus
Exercise 11.6 | Q 8 | Page 206

Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx

Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`

Integrate the following functions with respect to x :

`(x^3 + 4x^2 - 3x + 2)/x^2`

Integrate the following functions with respect to x :

(2x – 5)(3x + 4x)

Integrate the following functions with respect to x :

`(3x + 4) sqrt(3x + 7)`

Integrate the following functions with respect to x :

`1/(sqrt(x + 3) - sqrt(x - 4))`

Integrate the following with respect to x :

`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`

Integrate the following with respect to x :

`cot x/(log(sin x))`

Integrate the following with respect to x :

`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`

Integrate the following with respect to x :

`tan x sqrt(sec x)`

Integrate the following with respect to x:

x sin 3x

Integrate the following with respect to x:

`(x sin^-1 x)/sqrt(1 - x^2)`