# Thread: Integral with partial fractions

1. ## Integral with partial fractions

so I got

A= -3 , B = 5 C = 5

and i got ∫-3/x-4 + 5x+5/x²+9 dx for my equation

my answer came out to be

I dont know why it is wrong.

2. I didn't check the details but one mistake is that it should be $\displaystyle -3\ln(x-4)$, not $\displaystyle -3\ln(x+4)$

3. Originally Posted by emurphy

so I got

A= -3 , B = 5 C = 5

and i got ∫-3/x-4 + 5x+5/x²+9 dx for my equation

my answer came out to be

I dont know why it is wrong.
As well as the mistake already mentioned (which may well be just a typo), your calculation of $\displaystyle \int \frac{5x + 5}{x^2 + 9} \, dx$ is very wrong. Please show all the details of your calculation so that it can be reviewed.

4. Oh yeah that is pretty bad. Use parentheses! You wrote $\displaystyle 3/x-4 + 5x+5/x^2 + 9$ and integrated it as $\displaystyle 3/(x-4) + 5x+5/(x^2 + 9)$ when in fact you should have written $\displaystyle 3/(x-4) + (5x+5)/(x^2 + 9)$. These expressions are completely different from one another.

5. For $\displaystyle \int \frac{5x + 5}{x^2 + 9} \, dx$

I separated the fraction into 2

∫5x+5 dx + ∫1/x²+9 dx

∫5x+5 dx = 5x²/2+5x

∫1/x²+9 dx = ∫1/(1/9)(x²+1) dx = 9 ∫ 1/x²+1
= 9tan^-1(x)

6. Originally Posted by emurphy
For $\displaystyle \int \frac{5x + 5}{x^2 + 9} \, dx$

I separated the fraction into 2

∫5x+5 dx + ∫1/x²+9 dx

∫5x+5 dx = 5x²/2+5x

∫1/x²+9 dx = ∫1/(1/9)(x²+1) dx = 9 ∫ 1/x²+1
= 9tan^-1(x)
NO! You cannot seperate the integrand like that!! Using this logic you would solve $\displaystyle \int \frac{x}{x} \, dx$ as $\displaystyle \int x \, dx + \int \frac{1}{x} \, dx$ which is clearly so wrong that I don't need to say anything more.

7. Originally Posted by mr fantastic
NO! You cannot seperate the integrand like that!! Using this logic you would solve $\displaystyle \int \frac{x}{x} \, dx$ as $\displaystyle \int x \, dx + \int \frac{1}{x} \, dx$ which is clearly so wrong that I don't need to say anything more.
Adding to this, as a diagnostic of where you're at could you please do the following two integrals:

$\displaystyle I_1 = \int \frac{2x}{x^2 + 9} \, dx$

$\displaystyle I_2 = \int \frac{5}{x^2 + 9} \, dx$

Edit: If you cannot do these there is little point in you attempting questions like the one you posted until you have thoroughly reviewed the basic integration techniques this questions assumes and have developed a more solid understanding of integration.