In the integral ∫ (3x^2 + 2)^5 * 6x dx, what should be chosen as u for substitution?

Let $g\left(x\right)$ be a differentiable function. What is $\int 2g\left(x\right)g^{\prime }\left(x\right)dx$?

Evaluate the integral.

${\int }_0^1\frac{3x^2}{1+x^6}dx$

Evaluate the integral: ${\int }_0^{\frac{\pi }{3}}({\tan }^2\theta -2\tan \theta +5){\sec }^2\theta d\theta$

Compute the definite integral using trigonometric substitution:

${\int }_{8\sqrt{3}/2}^8\sqrt{64-x^2}dx$