Question

`int sin^-1 x`dx = ?

Options

• x sin^-1 x - `sqrt(1 + x^2)` + C

• x sin^-1 x - `sqrt(1 - x^2)` + C

• x sin^-1 x + `sqrt(1 - x^2)` + C

• x sin^-1 x + `sqrt(1 + x^2)` + C

Answer 1

x sin^-1 x + `sqrt(1 - x^2)` + C

Explanation:

We have,

I = `int sin^-1`x dx

I = `sin^-1 x int "dx" - int ("d"(sin^-1 x))/"dx" int "dx" * "dx"` + C

I = `x sin^-1 x - int 1/(sqrt(1 - x^2)) xx x "dx"` + C

I = `x sin^-1 x - int "2x"/(2 sqrt(1 - x^2))`dx + C

I = x sin^-1 x + `sqrt(1 - x^2)` + C