Compute the integral

by RoRi

August 20, 2015

Compute the following integral:

$\int_x^{x^2} (t^2+1)^2 \, dt.$

We have

$\begin{align*} \int_x^{x^2} (t^2+1)^2 \, dt &= \int_x^{x^2} (t^4 + 2t^2 + 1) \, dt \\ &= \left. \left( \frac{t^5}{5} + \frac{2t^3}{3} + t \right) \right|_x^{x^2} \\ &= \left( \frac{x^{10}}{5} + \frac{2x^6}{3} + x^2 \right) - \left( \frac{x^5}{5} + \frac{2x^3}{5} + x \right) \\ &= \frac{x^{10}}{5} + \frac{2x^6}{3} - \frac{x^5}{5} - \frac{x^3}{3} + x^2 - x. \end{align*}$

One comment

July 10, 2017 at 8:29 pm

123456grimmjaw says:

I think the x^3/3 is missing a two on the last line.

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Stumbling Robot

Compute the integral

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