Help with solving the following integral

**chrisn30** · Feb 6th 2013, 07:03 AM

Hi all,
Any help with the following integral would be much appreciated.

$\int(5x^2+\sqrt x-\frac{4}{x^2})dx$
This what i have so far
$\int \left ( 5x^2+\sqrt{x}-\frac{4}{x^2} \right )dx=\int 5x^2 dx+\int\sqrt{x}dx-\int\frac{4}{x^2}dx$
$5\int x^2 dx+\int x^\frac{1}{2}dx-4\int x^-^2 dx$
$5\int(\frac{x^3}{3})+(x^\frac{3}{2}/\frac{3}{2})-4x^-^1+c$
Am I somewhere close with what i have so far?

**earthboy** · Feb 6th 2013, 07:12 AM

Originally Posted by chrisn30

Hi all,
Any help with the following integral would be much appreciated.

$\int(5x^2+\sqrt x-\frac{4}{x^2})dx$
This what i have so far
$\int \left ( 5x^2+\sqrt{x}-\frac{4}{x^2} \right )dx=\int 5x^2 dx+\int\sqrt{x}dx-\int\frac{4}{x^2}dx$
$5\int x^2 dx+\int x^\frac{1}{2}dx-4\int x^-^2 dx$
$5\int(\frac{x^3}{3})+(x^\frac{3}{2}/\frac{3}{2})-4x^-^1+c$
Am I somewhere close with what i have so far?

Yes... everything you have done is correct except the typos(the integration sign) you have made in the last step..
$\displaystyle \frac{5x^3}{3}+\frac{2x^{\frac{3}{2}}}{3}+\frac{4} {x}+c$

**chrisn30** · Feb 6th 2013, 07:33 AM

Thanks for the help.

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