Integration of a function with it's derivative.

[hms.tech]

Homework Statement

Please help me by pointing me in the right direction for this integral :

∫ t^3 * (t^2 + 1)^0.5 dt

Homework Equations

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

http://www.sosmath.com/calculus/integration/byparts/img9.gif

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.

 

[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