# Thread: Integrating a fraction

1. ## Integrating a fraction

Hi there,

can somebody help me to integrate the following:

$\displaystyle \int\frac{1}{2y^{\frac{5}{4}}}dy$

I've used Mathcad to find that the answer is

$\displaystyle \frac{-2}{y^{\frac{1}{4}}}$

But I don't know any formulas or equations to use to get to the answer.

I would really appreciate any help.

Thanks.

2. ## Re: Integrating a fraction

Originally Posted by Srengam
Hi there,

can somebody help me to integrate the following:

$\displaystyle \int\frac{1}{2y^{\frac{5}{4}}}dy$

I've used Mathcad to find that the answer is

$\displaystyle \frac{-2}{y^{\frac{1}{4}}}$

But I don't know any formulas or equations to use to get to the answer.

I would really appreciate any help.

Thanks.

$\displaystyle \int\frac{1}{2y^{\frac{5}{4}}}dy=\frac{1}{2}\int y^{-\frac{5}{4}}dy$

3. ## Re: Integrating a fraction

Originally Posted by Srengam
Hi there,

can somebody help me to integrate the following:

$\displaystyle \int\frac{1}{2y^{\frac{5}{4}}}dy$

I've used Mathcad to find that the answer is

$\displaystyle \frac{-2}{y^{\frac{1}{4}}}$

But I don't know any formulas or equations to use to get to the answer.

I would really appreciate any help.

Thanks.
First write the integral using a negative index before applying the
power rule of integration.

$\displaystyle \frac{1}{2}\int{\frac{1}{y^{\frac{5}{4}}}dy=\frac{ 1}{2}\int{y^{-\frac{5}{4}}}dy$

Now increase the index of y by 1 and divide by the new index.

4. ## Re: Integrating a fraction

Originally Posted by Archie Meade

Now increase the index of y by 1 and divide by the new index.

5. ## Re: Integrating a fraction

Sorry, now I can't understand how to do the integration

$\displaystyle \int y^{-\frac{5}{4}}dy=\frac{-4}{y^{\frac{1}{4}}}$

I don't what equation or formula to use? I've never had the integrate a fractional power before, and can't find how anywhere in my notes.

Thanks.

6. ## Re: Integrating a fraction

Originally Posted by Srengam
Sorry, now I can't understand how to do the integration

$\displaystyle \int y^{-\frac{5}{4}}dy=\frac{-4}{y^{\frac{1}{4}}}$

I don't what equation or formula to use? I've never had the integrate a fractional power before, and can't find how anywhere in my notes.

Thanks.
same as the rule for any other exponent (except -1) ...

$\displaystyle \frac{y^{-\frac{5}{4} + 1}}{-\frac{5}{4} + 1} + C$

7. ## Re: Integrating a fraction

Thanks all,

I've been able to work through it now with your help.