Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Find an anti derivative (or integral) of the following function by the method of inspection.

(axe + b)²

Find an antiderivative (or integral) of the following function by the method of inspection.

sin 2x – 4 e^3x

Find the following integrals:

`int (4e^(3x) + 1)`

Find the following integrals:

`intx^2 (1 - 1/x^2)dx`

Find the following integrals:

`int (ax^2 + bx + c) dx`

Find the following integrals:

`int(2x^2 + e^x)dx`

Find the following integrals:

`int(sqrtx - 1/sqrtx)^2 dx`

Find the following integrals:

`int (x^3 + 5x^2   -4)/x^2 dx`

Find the following integrals:

`int (x^3 + 3x + 4)/sqrtx dx`

Find the following integrals:

`int (x^3 - x^2 + x - 1)/(x - 1) dx`

Find the following integrals:

`int(1 - x) sqrtx dx`

Find the following integrals:

`intsqrtx( 3x^2 + 2x + 3) dx`

Find the following integrals:

`int(2x - 3cos x + e^x) dx`

Find the following integrals:

`int(2x^2 - 3sinx + 5sqrtx) dx`

Find the following integrals:

`intsec x (sec x + tan x) dx`

Find the following integrals:

`int(sec^2x)/(cosec^2x) dx`

Find the following integrals:

`int (2 - 3 sinx)/(cos^2 x) dx.`

The anti derivative of `(sqrtx + 1/ sqrtx)` equals:

If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.

Integrate the function:

`1/(x - x^3)`