Answer to Question #346639 in Calculus for Main

Question

2. ∫ 12𝑥² √4𝑥³ + 7𝑑𝑥

Answer 1

$$\int12x^2\sqrt{4x^3+7}dx$$

$u=4x^3+7, du=12x^2dx$

$$\int12x^2\sqrt{4x^3+7}dx=\int\sqrt{u}du=\dfrac{2}{3}u^{3/2}+C$$

$$=\dfrac{2}{3}(4x^3+7)^{3/2}+C$$