Evaluate $\int x(7-5x^2)^5dx$ using u substitution

50 Views Asked by user637978 At 06 Apr 2026 - 5:30

Section 5.2

Can somebody verify this solution for me?? Thanks

Let $u=7-5x^2$. Then $\frac{du}{dx}=-10x$ and so $\frac{du}{-10x}=dx$. Making these substitutions we get:

$\int x(7-5x^2)^5dx$

$=\int x(u)^5 \frac{du}{-10x}$

$=\frac{1}{-10} \int u^5du$

$=\frac{1}{-10} u^6 \frac{1}{6} + C$

$=\frac{-1}{60} u^6 +C$

$= \frac{-1}{60} (7-5x^2)^6 +C$