Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Integrate the rational function:

`x/((x^2+1)(x - 1))`

Integrate the rational function:

`x/((x -1)^2 (x+ 2))`

Integrate the rational function:

`(3x + 5)/(x^3 - x^2 - x + 1)`

Integrate the rational function:

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

Integrate the rational function:

`(5x)/((x + 1)(x^2 - 4))`

Integrate the rational function:

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

Integrate the rational function:

`2/((1-x)(1+x^2))`

Integrate the rational function:

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

Integrate the rational function:

`1/(x^4 - 1)`

Integrate the rational function:

`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by x^{n − 1} and put xⁿ = t]

Integrate the rational function:

`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]

Integrate the rational function:

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

Integrate the rational function:

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

Integrate the rational function:

`1/(x(x^4 - 1))`

Integrate the rational function:

`1/(e^x -1)`[Hint: Put e^x = t]

`int (xdx)/((x - 1)(x - 2))` equals:

`int (dx)/(x(x^2 + 1))` equals:

Using properties of determinants, prove that 

`|(a^2 + 2a,2a + 1,1),(2a+1,a+2, 1),(3, 3, 1)| = (a - 1)^3`

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

Using properties of determinants, prove that `|(x,x+y,x+2y),(x+2y, x,x+y),(x+y, x+2y, x)| = 9y^2(x + y)`