HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Important Questions

If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______

`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 

`int sqrt(1 + sin2x)  dx`

`int cos^7 x  "d"x`

`int(log(logx))/x  "d"x`

`int ["cosec"(logx)][1 - cot(logx)]  "d"x`

`int (cos2x)/(sin^2x cos^2x)  "d"x`

If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)

`int ((x^2 + 2))/(x^2 + 1) "a"^(x + tan^(-1_x)) "d"x`

`int sqrt((9 + x)/(9 - x))  "d"x`

`int 1/(2 +  cosx - sinx)  "d"x`

`int sin(logx)  "d"x`

`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`

`int (x^2 + x -1)/(x^2 + x - 6)  "d"x`

`int (x + sinx)/(1 - cosx)  "d"x`

Evaluate:

`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`

`int  ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1])  "d"x`

Evaluate: `int (dx)/(2 + cos x - sin x)`

If u and v ore differentiable functions of x. then prove that:

`int uv  dx = u intv  dx - int [(du)/(d) intv  dx]dx`

Hence evaluate `intlog x  dx`

`int cos^3x  dx` = ______.