HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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)`

Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`

Choose the correct options from the given alternatives :

If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =

Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`

Integrate the following w.r.t. x: `(2x^2 - 1)/(x^4 + 9x^2 + 20)`

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

Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`

Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`

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

Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`

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

Integrate the following w.r.t.x:

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

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

Integrate the following w.r.t.x :  `sec^2x sqrt(7 + 2 tan x - tan^2 x)`

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

Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`

Solve the following differential equation:

`dy/dx + y/x = x^3 - 3`

Solve the following differential equation:

`cos^2 "x" * "dy"/"dx" + "y" = tan "x"`