HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Integrate the following functions with respect to x :

cos 3x cos 2x

Integrate the following functions with respect to x :

sin² 5x

Integrate the following functions with respect to x :

`(1 + cos 4x)/(cos x - tan x)`

Integrate the following functions with respect to x :

`"e"^(x log "a") "e"^x`

Integrate the following functions with respect to x :

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

Integrate the following functions with respect to x :

`(8^(1 + x) + 4^(1 - x))/2^x`

Integrate the following functions with respect to x :

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

Integrate the following functions with respect to x :

`(x + 1)/((x + 2)(x + 3))`

Integrate the following functions with respect to x :

`1/((x - 1)(x + 2)^2`

Integrate the following functions with respect to x :

`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`

Integrate the following functions with respect to x :

`x^3/((x - 1)(x - 2))`

Integrate the following with respect to x :

`x/sqrt(1 + x^2)`

Integrate the following with respect to x :

`x^2/(1 + x^6)`

Integrate the following with respect to x :

`("e"^x - "e"^-x)/("e"^x + "e"^-x)`

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 :

`(sin sqrt(x))/sqrt(x)`

Integrate the following with respect to x :

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

Integrate the following with respect to x :

`("cosec"  x)/(log(tan  x/2))`

Integrate the following with respect to x :

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

Integrate the following with respect to x :

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