How Do You Integrate Using Partial Fractions and Trig Substitution?

[aselin0331]

Homework Statement

[tex]\int(5x+2)/(x^{2}+25)^{2}dx[/tex]

Homework Equations

The Attempt at a Solution

[tex]\int5x/(x^{2}+25)^{2}dx+2\int1/(x^{2}+25)^{2}dx[/tex]

I can integrate the first part using u substitution then I am stuck at the second part...my partial fraction answer is the same as the question when I use the Ax+b, Cx+D thing...

I think it looks like an arc tan but I don't know how to go from there..

Thank you!

 

[tiny-tim]

hi aselin0331! welcome to pf!

for the second integral, use a trig substitution ​

 

[Mark44]

Homework Statement

[tex]\int(5x+2)/(x^{2}+25)^{2}dx[/tex]

Homework Equations

The Attempt at a Solution

[tex]\int5x/(x^{2}+25)^{2}dx+2\int1/(x^{2}+25)^{2}dx[/tex]

I can integrate the first part using u substitution then I am stuck at the second part...my partial fraction answer is the same as the question when I use the Ax+b, Cx+D thing...

I think it looks like an arc tan but I don't know how to go from there..

Thank you!

A trig substitution will work. Let x = 5 tan t, so dx = 5 sec²(t) dt.