Question

Find the indefinite integral. integral sign x^2times sqrt of x+5

Answer 1

\[\int\limits_{?}^{?} x ^{2}\sqrt{x+5}\]

Answer 2

using u substitution

Answer 3

u-sub

u^2=x+5 --------->> x=u^2-5
2udu=dx

\[\int\limits_{}^{}(u^2-5)^2u(2udu)\]
\[\int\limits_{}^{}(u^4-10u^2+25)u(2udu)\]
\[2\int\limits_{}^{}(u^4-10u^2+25)u^2du\]
\[2\int\limits\limits_{}^{}(u^6-10u^4+25u^2)du\]
\[2[\frac{u^7}{7}-\frac{10u^5}{5}+\frac{25u^3}{3}]+C\]
\[2[\frac{(x+5)^{7/2}}{7}-2(x+5)^{5/2}+\frac{25(x+5)^{3/2}}{3}]+C\]

Answer 4

Ohh! got it! thank u sam!:)