Recent content by kostas

Ah..so true :) Thank you!

Homework Statement Prove that \int cos^mxdx = \frac{cos^{m-1}x sinx}{m} + \frac{m-1}{m}\int cos^{m-2}xdx Homework Equations \int f(x)g'(x) = f(x)g(x) - \int g(x)f'(x) dx The Attempt at a Solution Going through any of the integrals provides constants that seem to be a problem...

Thank you all!

Homework Statement \lim_{x\to +\infty} \frac{x}{\sqrt{x^2+1}} Homework Equations The Attempt at a Solution \lim_{x\to +\infty} \frac{x}{\sqrt{x^2+1}} \stackrel{l'H}{=} \lim_{x\to +\infty} \frac{\sqrt{x^2+1}}{x} \stackrel{l'H}{=} \lim_{x\to +\infty} \frac{x}{\sqrt{x^2+1}}...

Yes, it was. I was making a silly mistake. Thanks!

Homework Statement Calculate the integral: \int x \frac{dx}{\sqrt{(a^2+x^2)^3}} where a\in R Homework Equations The Attempt at a Solution I solved "similar" integrals like \int \frac{dx}{\sqrt{a^2+x^2}} and \int \frac{dx}{x(x^2+1)} but none of the approaches I know (and...