HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following integrals: `int sin 4x cos 3x dx`

Evaluate the following integrals:

`int x/(x + 2).dx`

Evaluate the following integral: 

`int(4x + 3)/(2x + 1).dx`

Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`

Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`

Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`

Evaluate the following integrals:

`int (sin4x)/(cos2x).dx`

Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`

Evaluate the following integrals : `int cos^2x.dx`

Evaluate the following integrals:

`int(2)/(sqrt(x) - sqrt(x + 3)).dx`

Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`

If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)

Integrate the following functions w.r.t. x : `(logx)^n/x`

Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`

Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`

Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`

Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`

Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`

Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`

Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`