Integrate $\int \frac{14x}{(9+x^2)^3}dx$ using u-substitution

44 Views Asked by user637978 At 06 Apr 2026 - 7:09

Section 5.2: Can somebody Verify this solution for me?

Let $u=9+x^2$. Then $\frac{du}{dx}=2x$ and so $\frac{du}{2x}=dx$. Making these substitutions we get:

$\int \frac{14x}{(9+x^2)^3}dx$

$= \int \frac{14x}{u^3}\frac{du}{2x}$

$= \int \frac{7}{u^3}du$

$=7 \int u^{-3}du$

$=7 \frac{u^{-2}}{-2} + C$

$=\frac{-7}{2} (9+x^2)^{-2} + C$