1. ## integral x^3*cos(x^2)

my sheet says integrate by substitution then by parts. feeling a little stumped by the substitution guess i should have paid a little better attention in class.

intergal (x^3)(cos(x^2))dx

2. Originally Posted by kyle89
my sheet says integrate by substitution then by parts. feeling a little stumped by the substitution guess i should have paid a little better attention in class.

intergal (x^3)(cos(x^2))dx
Hi

Substitute $u=x^2 \Rightarrow du = 2x\:dx$

$\int x^3 \: \cos(x^2)dx = \int u \cos u \:\frac{du}{2}$

3. Originally Posted by kyle89
my sheet says integrate by substitution then by parts. feeling a little stumped by the substitution guess i should have paid a little better attention in class.

intergal (x^3)(cos(x^2))dx
Let $p=x^2$

$dp = 2x dx$

$\int x^3 \cos(x^2)dx = \int p \cos p \:\frac{dp}{2}$

4. integral (x^3)cos(x^2)=(1/2)integral ucos(u)du
let u=cos(u) du=-usin(u)
dv=u v=1/2 u^2
=(1/2)((1/2 u^2)cos(u)-integral (((1/2)u^2)(-usin(u))du)
=(1/2)((1/2 u^2)cos(u)+(1/2)integral((u^2)(usin(u))du)
=(1/2)((1/2)(((u^2)cos(u)+integral((u^3)sin(u)du)

than what comes after that? or am i missing something here?
also how do i make the integral sign and put things to a power?

5. $\int ucosudu = usinu + cosu$