Integral for a differential equation problem

[sihag]

i'm stuck on this relatively simply integral for a differential equation problem ...

| du / cos(pi/4 - u )
where | denotes the integral sign

some help ?

 

[tiny-tim]

∫ du / cos(π/4 - u)

Hi sihag!

Hint: substitute v = u - π/4.

(and copy the symbols below for future use! )

 

[Gib Z]

After letting $\frac{\pi}{4} - u =x$, all you need to know is $$\int \frac{1}{\cos x} dx = \log_e | \frac{1+\sin x}{\cos x} | + C$$.