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

Evaluate `int (x^2 + x)/(x^4 - 9) "d"x`

If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4e^x + 5e –x| + C, then ______.

If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.

Verify the following:

`int (x - 1)/(2x + 3) "d"x = x - log |(2x + 3)^2| + "C"`

Verify the following:

`int (2x + 3)/(x^2 + 3x) "d"x = log|x^2 + 3x| + "C"`

Evaluate the following:

`int ((x^2 + 2))/(x + 1) "d"x`

`int (cos2x - cos 2theta)/(cosx - costheta) "d"x` is equal to ______.

`int "e"^x ((1 - x)/(1 + x^2))^2  "d"x` is equal to ______.

`int x^9/(4x^2 + 1)^6  "d"x` is equal to ______.

`int x^3/(x + 1)` is equal to ______.

If `intx^3/sqrt(1 + x^2) "d"x = "a"(1 + x^2)^(3/2) + "b"sqrt(1 + x^2) + "C"`, then ______.

`int (x + 3)/(x + 4)^2 "e"^x  "d"x` = ______.

If A and B are invertible matrices of the same order, then (AB)^-1 is equal to ____________.

If `"x = a sin"  theta  "and  y = b cos"  theta, "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

If y `= "Ae"^(5"x") + "Be"^(-5"x") "x"  "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

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

Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`

The value of `int_2^3 x/(x^2 + 1)`dx is ______.

If A, B are non-singular square matrices of the same order, then (AB^–1)^–1 = ______.

If A and B are invertible square matrices of the same order, then which of the following is not correct?