Find the area below the graph of f, but f is in fractional form?

[LilTaru]

Homework Statement

Find the area below the graph of f.

f(x) = (2x + 5)/[(x + 2)²(x + 3)²] xE [0, 1]

Homework Equations

I know the area under the graph is the definite integral with upper limit = 1; lower limit = 0.

The Attempt at a Solution

I have such a hard time evaluating integrals when they are in fractional form. I know if G(x) is the antiderivative of f, then:

Area = G(1) - G(0)

But, I don't know how to find an antiderivative for f? It seems impossible to me! Someone please help!

 

[Char. Limit]

Have you tried partial fractions? They're going to be very useful here.

 

[LilTaru]

We never learned how to use them... Is there a website that shows how to use them?

 

[LilTaru]

Nevermind... Found a website with a similar question and a step-by-step guide of how to solve it and why! It was really helpful! Thanks for putting me on the right track!

 

[Char. Limit]

It was no problem. Have a great day!