hello,
can anyone please help intergrate this, i dont know how to do square root integration...
$\displaystyle
\int{x^5\sqrt{x^6+7}dx}
$
use substitution:
$\displaystyle u = {x^6}+7 \rightarrow du = 6x^5 dx \rightarrow dx = \frac{du}{6x^5} $
put the above in your integration:
$\displaystyle \int {x^5\sqrt{x^6+7}dx}$
= $\displaystyle \int{x^5\sqrt{u}} \frac{du}{6x^5}$
= $\displaystyle \int \frac{\sqrt{u}}{6} du $
solve
the part here where you solve for dx from du we havent been taught yet, but going along with the substitution you said i got to:$\displaystyle
u = {x^6}+7 \rightarrow du = 6x^5 dx \rightarrow dx = \frac{du}{6x^5}$
$\displaystyle
\frac{1}{6}\int{\sqrt{u}}
$
but what would the integration of that be??