Question

X^2(√(1+x))dx
I need your help with this integral

Answer 1

x squared times...
or ?

Answer 2

\[\int\limits_{}^{}\dfrac{x^2}{\sqrt{{1+x}}}dx\]

Answer 3

substitution

u = 1+x
du = dx

Answer 4

\[\int\limits_{}^{}\frac{(u-1)^2}{\sqrt{u}} du\]

Answer 5

\[= \int\limits \frac{u^2}{\sqrt{u}} -\frac{2u}{\sqrt{u}}+\frac{1}{\sqrt{u}}\]

Answer 6

another way: Let \(u =\sqrt{1+x}\), \(du=\dfrac{1}{2\sqrt{1+x}}dx\)
and \(u^2= 1+x --> x=u^2-1\rightarrow x^2= (u^2-1)^2\)
everything is ok from here.