HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Integrate the following with respect to x.

`("e"^(3x) - "e"^(-3x))/"e"^x`

Integrate the following with respect to x.

`("e"^(3x) +"e"^(5x))/("e"^x + "e"^-x)`

Integrate the following with respect to x.

`[1 - 1/2]"e"^((x + 1/x))`

Integrate the following with respect to x.

`1/(x(log x)^2`

Integrate the following with respect to x.

If f'(x) = e^x and f(0) = 2, then find f(x)

Integrate the following with respect to x.

2 cos x – 3 sin x + 4 sec²x – 5 cosec²x

Integrate the following with respect to x.

sin³x

Integrate the following with respect to x.

`(cos 2x + 2sin^2x)/(cos^2x)`

Integrate the following with respect to x.

`1/(sin^2x cos^2x) ["Hint:" sin^2x + cos^2x = 1]`

Integrate the following with respect to x.

`sqrt(1 - sin 2x)`

Integrate the following with respect to x.

xe^–x 

Integrate the following with respect to x.

x³e^3x

Integrate the following with respect to x.

log x

Integrate the following with respect to x.

x log x

Integrate the following with respect to x.

xⁿ log x

Integrate the following with respect to x.

`x^5  "e"^x`

Integrate the following with respect to x.

`(2x + 5)/(x^2 + 5x - 7)`

Integrate the following with respect to x.

`("e"^(3logx))/(x^4 + 1)`

Integrate the following with respect to x.

`"e"^(2x)/("e"^(2x) - 2)`

Integrate the following with respect to x.

`(log x)^3/x`