Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

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)`

Integrate the function:

`1/(sqrt(x+a) + sqrt(x+b))`

Integrate the function:

`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`

Integrate the function:

`1/(x^2(x^4 + 1)^(3/4))`

Integrate the function: 

`1/(x^(1/2) + x^(1/3))  ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))),  "put x" = t^6]`

Integrate the function:

`(5x)/((x+1)(x^2 +9))`