Commerce (English Medium) Class 12 - CBSE Important Questions

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:

Evaluate each of the following integral:

Evaluate : \[\int\limits_0^\pi/4 \frac{\sin x + \cos x}{16 + 9 \sin 2x}dx\] .

Evaluate : \[\int\limits_0^{2\pi} \cos^5 x dx\] .

Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .

Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .

Evaluate : \[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\] .

Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .

Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .

Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .

Evaluate: \[\int\limits_{- \pi/2}^{\pi/2} \frac{\cos x}{1 + e^x}dx\] .

Evaluate : \[\int e^{2x} \cdot \sin \left( 3x + 1 \right) dx\] .

Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .