Integral question (1 Viewer)

[Axio]

Hi guys, can anyone help me with this integral?



I know that there would be easier ways to solve it but can anyone see where I've gone wrong?

I use a trigonometric substitution and then integration by parts. Assuming my other steps are right, I get to:



And then by substituting in:



I get:



... Which doesn't seem to be the right answer :/.

EDIT:

I think my mistake is coming from substituting it back in...

 

[integral95]

Hi guys, can anyone help me with this integral?



I know that there would be easier ways to solve it but can anyone see where I've gone wrong?

I use a trigonometric substitution and then partial fractions. Assuming my other steps are right, I get to:



And then by substituting in:



I get:



... Which doesn't seem to be the right answer :/.

EDIT:

I think my mistake is coming from substituting it back in...

What trig substitution made you use partial fraction afterwards?








From there you use IBP (integration by parts) then you sub it back in.

(i dunno if that's the best method though lol)

 

[Axio]

Lol sorry I meant integration by parts... What does sec(tan^-1(x/4)) equal?

 

[astroman]

http://www.wolframalpha.com/input/?i=sec(tan^-1(x/4))

 

[InteGrand]

Lol sorry I meant integration by parts... What does sec(tan^-1(x/4)) equal?

(Use sec² t = 1 + tan² t)
(taking positive square root since sec is positive when the argument is between and , which it is here, since the argument is an inverse tan)