Hi. I need to integrate x times the square root of 3x. Is integration by parts usable in this case, and if so, can you please work it out (I am not supposed to use the simplification method and the power rule to solve it w/o integration by parts).

Thanks

2. Originally Posted by jaijay32
Hi. I need to integrate x times the square root of 3x. Is integration by parts usable in this case, and if so, can you please work it out (I am not supposed to use the simplification method and the power rule to solve it w/o integration by parts).

Thanks
I do not know what is the point of solving it with integration by parts.
Any way, take $u=\sqrt{3x}$ and $dv=xdx$
hence, $du=\frac{\frac{3}{2}}{\sqrt{3x}}dx$ and $v=\frac 1 2 x^2$

And apply the formula of integration by parts:
$\int u dv = uv - \int v du$.

3. Originally Posted by jaijay32
Hi. I need to integrate x times the square root of 3x. Is integration by parts usable in this case, and if so, can you please work it out (I am not supposed to use the simplification method and the power rule to solve it w/o integration by parts).

Thanks
Parts is overkill my friend.

$3x\sqrt{x}=3x^1x^{1/2}=3x^{1+1/2}=3x^{3/2}$

So, take $\int3x^{3/2}dx$ by way of the power rule