Question

Помогите решить итегралы

Answer 1

26.

$\int\limits {x}^{2} \sqrt[3]{1 + {x}^{3} } dx \\ \\ 1 + {x}^{3} = t \\3 {x}^{2} dx = dt \\ {x}^{2} dx = \frac{dt}{3} \\ \\ \frac{1}{3} \int\limits \sqrt[3]{t} dt = \frac{1}{3}\int\limits {t}^{ \frac{1}{3} } dt = \frac{1}{3} \times \frac{ {t}^{ \frac{4}{3} } }{ \frac{4}{3} } + C = \\ = \frac{1}{4} \sqrt[3]{ {t}^{4} } + C = \frac{1}{4} \sqrt[3]{ {(1 + {x}^{3}) }^{4} } + C$

27.

$\int\limits \sin(2x + 3) dx \\ \\ 2x + 3 = t \\ 2dx = dt \\ dx= \frac{dt}{2} \\ \\ \frac{1}{2} \int\limits \sin(t)dt = - \frac{1}{2} \cos(t) + C = \\ = - \frac{1}{2} \cos(2x + 3) + C$