## shaqadry Group Title integrate -x(1+2x)^5 dx one year ago one year ago

1. ash2326 Group Title

$\int -x(1+2x)^5dx$ We can expand (1+2x)^5, but that will be tiring Do you know u substitution method ?

how do i solve it by parts?

3. ash2326 Group Title

Not by parts, do u know u-substitution? It'll make it easy

4. ash2326 Group Title

@shaqadry Put 2x+1=t so $2dx=dt$ $dx=\frac{dt}{2}$ Do you get this?

yes!

and then?

wait but the question requires me to solve it by parts :-/

8. ash2326 Group Title

Then, we will use this $\int uv=u\int v-\int(du \int v)$

9. ash2326 Group Title

Can you try, apply it here?

@ash2326 which one should i equate to 'u' ? which is the better choice?

11. ash2326 Group Title

Equate x to u, it'll become 1 in the second part of by parts and then we find the integral easily @shaqadry