Would really appreciate if anyone could help me with this problem:
Clueless, please help! Thanks!
integral[xsec^2(x)] is required.
ok. I'd do integration by parts, forgive me if I screw this up, I have p3 on tues so it'll cost me!
let u = x
and let dv/dx=sec^2(x)
1. du/dx= 1
2. v = integral[dv/dx]=int[sec^2(x)]= tan (x)
3.now, assuming you're doing edexcel maths, turn to page 8 of the formulae sheet, look at the bottom expression in the 'integration' section.
You will see:
integral[u(dv/dx)dx] = uv - integral[v(du/dx)dx]
thus we have:
integral[xsec^2(x)]= x*tan(x)- int[tan(x) * 1]
Note that the integral of tan(x) is ln|sec(x)| + C
integral[xsec^2(x)]= xtan(x)- ln|sec(x)| + C
At least, I hope so! Or else Im in trouble.
x*(sec(X^2)), but i think what you integrated is right. Good luck.