Question

Calculus question: Find the indefinite integral using substitution and change of variables.

Answer 1

\[\int\limits_{}^{}x \]\[\sqrt{x+6}dx\]

Answer 2

^ The above problem should be together.
Could someone walk me through this problem?

Answer 3

this \[\int x\sqrt{x+6}\,\,dx\]
?

Answer 4

yes, when i tried to put the square root sign in, it went to the front of the integral sign. Thanks.

Answer 5

let \[u=x+6\]

\[du=dx\]
and \[x=u-6\]

\[\int x\sqrt{x+6}\,\,dx=\int (u-6)\sqrt{u}\,\,du=\cdots\]

Answer 6

you need more help than that?

Answer 7

I'll let you know, I'm gonna see if I can finish it from there

Answer 8

In my book before it simplifies the integral to get the final answer it gets this:
\[\int\limits_{}2/5 (x+6)^{5/2}-4(x+6)^{3/2}+C\]

I don't get how they got -4(x+6)^3/2

Answer 9

\[\int (u-6)\sqrt{u}\,\,du=\int(u^{3/2}-6u^{1/2})du\]
\[=\frac{2}{5}u^{5/2}-6\frac{2}{3}u^{3/2}+c=\frac{2}{5}u^{5/2}-4u^{3/2}+c\]

\[=\frac{2}{5}(x+6)^{5/2}-4(x+6)^{3/2}+c\]

Answer 10

oh okay, I see now. Thanks .