determine-the-indefinite-integral-by-performing-a-trigonometric-substitution-and

Question

Determine the indefinite integral by performing a trigonometric substitution: ∫x2(16+x2)2 dx \int \frac{$$x^2$$}{(16 + $$x^2$)^2$$} \, dx

Accepted Answer

18tan⁡−1x4−x2(16+x2)+C\frac{1}{8}\$$tan^{-1}$$\frac{x}{4}-\frac{x}{2\$$left(16+x^2$$\right)}+C

Answer

18tan⁡−1x4−x16+x2+C\frac{1}{8}\$$tan^{-1}$$\frac{x}{4}-\frac{x}{$$16+x^2$$}+C

Answer

tan⁡−1x4−x2(16+x2)+C\$$tan^{-1}$$\frac{x}{4}-\frac{x}{2\$$left(16+x^2$$\right)}+C

Answer

tan⁡−14x+x16+x2+C\$$tan^{-1}4x$$+\frac{x}{$$16+x^2$$}+C

Determine the indefinite integral by performing a trigonometric substitution: ∫x2(16+x2)2dx \(\int\) \(\frac{x^2}{(16 + x^2)^2}\) \, dx