Question

Me ajudem

Calcule a integral indefinida ∫(2ex + 3x1/2 + 4x)dx

Answer 1

Resposta:

C)

Explicação passo-a-passo:

$∫ \frac{ {x}^{4} + 3 {x}^{ - \frac{1}{2} } + 4 }{ {x}^{ \frac{1}{3} } } dx \\ ∫ \frac{ {x}^{4} }{ {x}^{ \frac{1}{3} } } dx + ∫ \frac{3 {x}^{ - \frac{1}{2} } }{ {x}^{ \frac{1}{3} } } dx + ∫ \frac{4}{ {x}^{ \frac{1}{3} } } dx \\ ∫ {x}^{4 - \frac{1}{3} } dx +3 ∫ {x}^{ - \frac{1}{2} - \frac{1}{3} }dx + 4∫ {x}^{ - \frac{1}{3} }dx \\ ∫ {x}^{ \frac{11}{3} } dx + 3∫ {x}^{ - \frac{5}{6} }dx + 4∫ {x}^{ - \frac{1}{3} } dx \\ \frac{ 3{x}^{ \frac{14}{3} } }{14} + 3 \times 6 {x}^{ \frac{1}{6} } + 4 \times \frac{3 {x}^{ \frac{2}{3} } }{2} + c \\ \frac{ 3{x}^{ \frac{14}{3} } }{14} + 18 {x}^{ \frac{1}{6} } + 6 {x}^{ \frac{2}{3} } + c$