Integration help

[koalasrock]

I'm having trouble starting the integral of x/(x^2+2x+26)

Any help will be appreciated!

Even 1 step will help.

 

[MarkFL]

I would consider rewriting the integrand as follows:

\(\displaystyle \dfrac{x}{x^2+2x+26}=\dfrac{(x+1)-1}{x^2+2x+26}=\dfrac{1}{2}\cdot\dfrac{2x+2}{x^2+2x+26}-\dfrac{1}{(x+1)^2+5^2}\)

Now, the first term is ripe for a u-substitution and the second term is ripe for a trigonometric substitution or the observation that its anti-derivative is a function of a particular inverse trig. function.

 

[Deleted member 4993]

I'm having trouble starting the integral of x/(x^2+2x+26)

Any help will be appreciated!

Even 1 step will help.

Another way - albeit less elegant way - would be to brute force "partial fraction" method.

 

[koalasrock]

Thank you so much! I know exactly where to go with it now.