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

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

  • 1
    $\begingroup$ Depends, what do you want this integral for? What was the original question? $\endgroup$
    – Kaynex
    Mar 12, 2017 at 0:24

1 Answer 1


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*}


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