# Integration by substitution

• February 8th 2010, 12:10 PM
renlok
Integration by substitution
i have the integral $\int csc(\pi x - 1) dx$
if i say $t = \pi x - 1 => dt = \pi dx$
so i make the substitution leaving $\frac{1}{\pi}\int csc(t) dt$

but ive no idea how to integrate cosec?
• February 8th 2010, 12:19 PM
driegert
$\int csc(x)dx = ln |csc(x)-cot(x)| + C$

I had to look it up in a table of values.

Trigonometric Integrals

Hope that helps.
• February 8th 2010, 12:25 PM
renlok
thanks i also found you can find it by multiplying it by $\frac{csc(x) + cot(x)}{csc(x) + cot(x)}$ (Hi)
• February 8th 2010, 01:37 PM
Krizalid
that "+" it's actually a "-". :D