Question

помогите найти интеграл 1 пример! ​

Answer 1

Ответ:

$∫ \sqrt{4 {x}^{3} + 1 } {x}^{2} dx = \frac{1}{3} ∫ \sqrt{4 {x}^{3} + 1 }3 \times 3{x}^{2} dx = \frac{1}{3} ∫ \sqrt{4 {x}^{3} + 1 } d( {x}^{3} ) = \frac{1}{3} \times \frac{1}{4} ∫ \sqrt{4 {x}^{3} + 1} d(4 {x}^{3} + 1) = \frac{1}{12} = \frac{ {(4 {x}^{3} + 1) }^{ \frac{3}{2} } }{ \frac{3}{2} } + c = \frac{2}{3} \sqrt{ {(4 {x}^{3} + 1) }^{3} } + c$