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

Evaluate the following.

`int 1/(4"x"^2 - 1)` dx

Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx

Evaluate the following.

`int 1/(4"x"^2 - 20"x" + 17)` dx

Evaluate the following.

`int x/(4x^4 - 20x^2 - 3) dx`

Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx

Evaluate the following.

`int 1/("a"^2 - "b"^2 "x"^2)` dx

Evaluate the following.

`int 1/(7 + 6"x" - "x"^2)` dx

Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx

Evaluate the following.

`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx

Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx

Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx

Choose the correct alternative from the following.

The value of `int "dx"/sqrt"1 - x"` is

`int sqrt(1 + "x"^2) "dx"` =

Choose the correct alternative from the following.

`int "x"^2 (3)^("x"^3) "dx"` =

`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?

Choose the correct alternative from the following.

`int "dx"/(("x" - "x"^2))`= 

Fill in the Blank.

`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x⁴ + ______ x³ + 5x + c

`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c

If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______

To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.