2
$\begingroup$

What is the integral of $x^{-2\theta}$?

Not sure how the integration works with two variables. Can anyone confirm?

$\endgroup$
  • 1
    $\begingroup$ Depends, what do you want this integral for? What was the original question? $\endgroup$ – Kaynex Mar 12 '17 at 0:24
5
$\begingroup$

You have to choose a variable to integrate, the other remains as a constant. Or do both, one at a time.

Integrating with respect to x: \begin{align*} \int x^{-2 \theta} dx &= \frac{x^{1 - 2\theta}}{1 - 2\theta} + C\\ \end{align*} Integrating with respect to θ: \begin{align*} \int x^{-2 \theta} d \theta &= -\frac{x^{-2 \theta}}{2 \ln(x)} + C \end{align*}

| cite | improve this answer | |
$\endgroup$

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.