Science (English Medium) इयत्ता १२ - CBSE Important Questions

Evaluate:

`int((x+3)e^x)/((x+5)^3)dx`

Find the particular solution of the differential equation x²dy = (2xy + y²) dx, given that y = 1 when x = 1.

find `∫_2^4 x/(x^2 + 1)dx`

Evaluate :   `∫1/(cos^4x+sin^4x)dx`

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.

Evaluate :

`int_e^(e^2) dx/(xlogx)`

Find `int dx/(5 - 8x - x^2)`

Find the following integrals:

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

Evaluate the definite integral:

`int_0^(pi/2) cos^2 xdx`

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/4) log (1+ tan x) dx`

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`

Find `int (cos theta)/((4 + sin^2 theta)(5 - 4 cos^2 theta)) d theta`

Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`

Find `int dx/(5 - 8x - x^2)`

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

Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`

Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx

Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`

Evaluate the following integral: