Question

`int sqrt(1 + x^2) dx` is equal to

Options

• `x/2 sqrt(1 + x^2) + 1/2 log|x + sqrt(1 + x^2)| + c`

• `2/3 (1 + x^2)^(3/2) + c`

• `2/3x (1 + x^2)^(3/2) + c`

• `x^2/2 sqrt(1 + x^2) + x^2/2 log |x + sqrt(1 + x^2)| + c`

Answer 1

`x/2 sqrt(1 + x^2) + 1/2 log|x + sqrt(1 + x^2)| + c`

Explanation:

We have, 

`int sqrt(a^2 + x^2)  dx = x/2 sqrt(a^2 + x^2) + a^2/2 log|x + sqrt(a^2 + x^2)| + c`

Here `a^2 = 1`

∴ `int sqrt(1 + x^2)  dx = x/2 sqrt(1 + x^2) + 1/2 log|x + sqrt(1 + x^2)| + c`