I try to evaluate this two integrals, but I don't know how to proceed:

i) $\int \sqrt{x\sqrt{2x}} dx = \int {2^{\frac{1}{4}}\cdot x^{\frac{3}{4}}}$

ii) $ \int 3^x e^x dx$

What's the best way to evaluate them? Substitution or Intergration by parts?

Any hints are appreciated.

  • $\begingroup$ Should ii) be as in the title or as in the question? $\endgroup$ – mrf Sep 12 '12 at 7:53
  • $\begingroup$ as in the title, I edited it, thanks. $\endgroup$ – ulead86 Sep 12 '12 at 7:58
  • 2
    $\begingroup$ You don't solve integrals, you evaluate them. $\endgroup$ – Stefan Smith Sep 12 '12 at 14:03

You’ll do better with the first one if you correct the algebra:


Now you have $\displaystyle\int2^{1/4}x^{3/4}~dx=2^{1/4}\int x^{3/4}~dx$, which is just a power rule integration.

In the second problem, use the fact that $3^xe^x=(3e)^x$; I’m sure that you’ve been shown how to integrate $a^x$ for a constant $a$.

You don’t need any special techniques for either of them.

  • $\begingroup$ Thanks a lot, I edited the mistake. And yes, I know how to integrate $a^x$. Thanks for the answer. $\endgroup$ – ulead86 Sep 12 '12 at 7:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.