Pretty simple Calculus questions

**Corum** · January 6th 2010, 01:34 PM

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

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

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

a hand on these will be very appreciated

**skeeter** · January 6th 2010, 03:10 PM

Originally Posted by Corum

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

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

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

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

partial fractions

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

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

$\int \frac{\sin^{-3}{x}}{\cot^3{x}} \, dx<br />$

use a some trig identities ...

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

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

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

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