HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If y = Ae^mx + Be^nx, show that y₂ – (m + n)y₁ + mny = 0.

Integrate the following w.r.t. x : `x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))`

Integrate the following w.r.t. x : `(12x + 3)/(6x^2 + 13x - 63)`

Integrate the following w.r.t. x : `(2x)/(4 - 3x - x^2)`

Integrate the following w.r.t. x : `(x^2 + x - 1)/(x^2 + x - 6)`

Integrate the following w.r.t. x:

`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`

Integrate the following w.r.t. x : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`

Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`

Integrate the following w.r.t. x : `(2x)/((2 + x^2)(3 + x^2)`

Integrate the following w.r.t. x : `2^x/(4^x - 3 * 2^x - 4`

Integrate the following w.r.t. x : `(3x - 2)/((x + 1)^2(x + 3)`

Integrate the following w.r.t. x : `(5x^2 + 20x + 6)/(x^3 + 2x ^2 + x)`

Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`

Integrate the following w.r.t. x : `(1)/(x^3 - 1)`

Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`

Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`

Integrate the following w.r.t. x : `(1)/(2sinx + sin2x)`

Integrate the following w.r.t. x : `(1)/(sin2x + cosx)`

Integrate the following w.r.t. x : `(1)/(sinx*(3 + 2cosx)`

Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`