Better Students Ask More Questions.
Q. `int` `(x^2 - 1)/(x^2 + 1)` `dx` `=?`
1 Answer | add yours
High School Teacher
Best answer as selected by question asker.
Notice that the degree of the numerator and denominator are the same. So, before we integrate, expand `(x^2-1)/(x^2+1)` .
Using long division,
Then, express it as difference of two integrals.
`=intdx - int 2/(x^2+1)dx`
For the first integral, apply the formula `int kdx=kx+C` .
`=x+C -int 2/(x^2+1)dx`
For the second integral, apply the formula `int1/(x^2+a^2)dx=1/a tan^(-1) x/a` .
`=x+C -2int 1/(x^2+1)dx`
Since C represents any number, express the sum of the C's as C only.
Hence, `int(x^2-1)/(x^2+1)dx=x-2tan^(-1)x+C` .
Posted by mjripalda on July 12, 2013 at 2:17 AM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.