# Thread: Pretty simple Calculus questions

1. ## Pretty simple Calculus questions

Hello. First post on this forum. I have an assortment of questions, hope somebody can help me.
first: $\displaystyle \int \frac{1}{x^3+x} dx$

second: $\displaystyle \int \sqrt{1-x^2} dx$

third: $\displaystyle \int$$\displaystyle \frac{1}{ sin^2 cot^3} dx$

a hand on these will be very appreciated

2. Originally Posted by Corum
Hello. First post on this forum. I have an assortment of questions, hope somebody can help me.
first: $\displaystyle \int_ (1/x^3+x) dx$

second: $\displaystyle \int$ (1-x^2)^(1/2)dx (that's trying to be a sqr root)

third: $\displaystyle \int$(sin^-3 x / cot^3) dx

$\displaystyle \int \frac{1}{x(x^2+1)} \, dx$

partial fractions

$\displaystyle \int \sqrt{1-x^2} \, dx$

try a trig sub ... $\displaystyle x = \sin{\theta}$

$\displaystyle \int \frac{\sin^{-3}{x}}{\cot^3{x}} \, dx$

use a some trig identities ...

$\displaystyle \frac{\sin^{-3}{x}}{\cot^3{x}} = \sec^3{x}$

$\displaystyle \int \sec^3{x} \, dx$

use parts ... $\displaystyle u = \sec{x}$ , $\displaystyle dv = \sec^2{x} \, dx$