Home » Blog » Compute the vector valued integral Compute the vector valued integral by RoRi June 1, 2016 Compute the vector valued integral We compute, Related
![\[ \int_0^1 \left( \frac{e^t}{1+e^t} \mathbf{i} + \frac{1}{1+e^t} \mathbf{j} \right) \, dt.\]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-878d4d270af0e957e140ad2a90793518_l3.png "Rendered by QuickLaTeX.com")
![\begin{align*} \int_0^1 \left( \frac{e^t}{1+e^t} \mathbf{i} + \frac{1}{1+e^t} \mathbf{j} \right) \,dt &= \left( \int_0^1 \frac{e^t}{1+e^t} \, dt \right) \mathbf{i} + \left( \int_0^1 \frac{1}{1+e^t} \, dt \right) \mathbf{j} \\[9pt] &= \log \left( \frac{1+e}{2} \right) \mathbf{i} + \left( 1 - \log \frac{1+e}{2} \right) \mathbf{j}. \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-767265fe2a4b8fbad9625d0e53bc986b_l3.png "Rendered by QuickLaTeX.com")