Question

Determina la integral de las siguientes funciones

Answer 1

Respuesta:

$1) \int( - 2 {x}^{ \frac{2}{3} } + 5 \sqrt{x} - 3 + {x}^{ \frac{3}{2} } )dx = - 2\int{x}^{ \frac{2}{3} }dx + 5\int {x}^{ \frac{1}{2} } dx - 3\int dx + \int {x}^{ \frac{3}{2} } dx \\ = - 2( \frac{3}{5} ) {x}^{ \frac{5}{3} } + 5( \frac{2}{3} ) {x}^{ \frac{3}{2} } - 3x + \frac{2}{5} {x}^{ \frac{5}{2} } + k \\ = - \frac{6}{5} {x}^{ \frac{5}{3} } + \frac{10}{3} {x}^{ \frac{3}{2} } - 3x + \frac{2}{5} {x}^{ \frac{5}{2} } + k$

$3) \int( 4 {x}^{ 2} - 2 \sqrt{x} )( {x}^{ - 1} )dx = \int( 4 x - 2 {x}^{ \frac{ - 1}{2} } )dx \\ = 4\int{x}dx - 2\int {x}^{ \frac{ - 1}{2} } dx \\ = 4( \frac{1}{2} ) {x}^{2} - 2(2) {x}^{ \frac{1}{2} } + k \\ = 2{x}^{2} - 4 \sqrt{x} + k$