HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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 (sin4x)/(cos 2x) "d"x`

`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`

`int logx/x  "d"x`

`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`

`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`

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

`int x^x (1 + logx)  "d"x`

`int 1/(xsin^2(logx))  "d"x`

`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`

`int (cos2x)/(sin^2x)  "d"x`

`int cot^2x  "d"x`

`int x/(x + 2)  "d"x`

`int cos^7 x  "d"x`

`int(log(logx))/x  "d"x`

`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`

Select and write the correct alternative from the given option for the question

Solution of the equation `x  ("d"y)/("d"x)` = y log y is

The general solution of `(dy)/(dx)` = e^−x is ______.