Integral is it Partial Fraction

[whatlifeforme]

Homework Statement

Evaluate the integral.

Homework Equations

$\displaystyle\int_0^∞ {\frac{dv}{(1+v^2)(1+arctanv)}}$

The Attempt at a Solution

i am not sure how to do partial fractions with an inverse trig function in the denominator.

i tried v=arctanv so i could do a substitution, but that would be correct, and i don't know how using another variable would work such as z=arctanv.

 

[slider142]

The letter you use for your substitution does not have to be any special letter, as long as it doesn't confuse you. If you feel like it, write arctan(v) as z. However we now need to write the entire integral in terms of z and we need dz if we want to integrate it in this form. If z = arctan(v), then what is dz ? Is dz present in the integral ?

 

[Dick]

Homework Statement

Evaluate the integral.

Homework Equations

$\displaystyle\int_0^∞ {\frac{dv}{(1+v^2)(1+arctanv)}}$

The Attempt at a Solution

i am not sure how to do partial fractions with an inverse trig function in the denominator.

i tried v=arctanv so i could do a substitution, but that would be correct, and i don't know how using another variable would work such as z=arctanv.

v=arctan(v) is nonsense. z=arctan(v) should work. Try it.