Homework Help: Integration of a function with it's derivative.

1. Jan 23, 2012

hms.tech

1. The problem statement, all variables and given/known data

∫ t^3 * (t^2 + 1)^0.5 dt

2. Relevant equations

i used the standard formula of integration by parts on this.

http://www.sosmath.com/calculus/integration/byparts/img9.gif
3. The attempt at a solution

here is what is did :
1/2∫ 2t * t^2 * (t^2 + 1)^0.5 dt
1/2{ [t^2 * (t^2 + 1)^1.5 * 2/3] - [∫ 2t * (t^2 + 1)^1.5 * 2/3 dt ]}

i highly doubt it is correct, i think i used the formula wrongly.

Can anyone point out my mistake or just provide me with any other sort of help, it would be appreciated.

2. Jan 23, 2012

ehild

The title of your thread is "Integration of a function with it's derivative". The integral can be written as

$$\int{t^3(t^2+1)^{0.5} dt}=0.5\int{((t^2+1)-1)(t^2+1)^{0.5} (2tdt)}$$ .

Apply "integration by substitution".

$$\int{f(g(x))g'(x)dx}=\int{f(g)dg}$$

ehild