1. ## integrating

hello,

$\displaystyle \int{x^5\sqrt{x^6+7}dx}$

2. Originally Posted by drewbear
hello,

$\displaystyle \int{x^5\sqrt{x^6+7}dx}$
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

3. $\displaystyle u = {x^6}+7 \rightarrow du = 6x^5 dx \rightarrow dx = \frac{du}{6x^5}$
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:

$\displaystyle \frac{1}{6}\int{\sqrt{u}}$

but what would the integration of that be??

4. Originally Posted by drewbear
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:

$\displaystyle \frac{1}{6}\int{\sqrt{u}}$

but what would the integration of that be??
$\displaystyle \frac{1}{6}\int{\sqrt{u}}$

$\displaystyle = \frac{1}{6}\int u^{\frac{1}{2}} du$

$\displaystyle = \frac{1}{6} \times [ \frac{2}{3} \times {u^{\frac{3}{2}}}] + C$

Now substitute the value of $\displaystyle u = {x^6}+7$ in the above equation