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Evaluate the integral by making the given substitution. $\displaystyle \int \sqrt{2t + 1} \, dt$, $u = 2t + 1$

$\frac{(2 t+1)^{3 / 2}}{3}+C$

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Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Boston College

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Video Transcript

we know that we've been given you is to t plus one. Therefore, we know he can write this as d'you this to d t. Which means that de t written by itself is do you divide by two or 1/2 to you? Now remember, with into girls, you can always pull out the constant like this. So one half's on the outside and truth is using the power rule the exploding increases by one divide by the new exploit which, as you can see his three over two back substitute and I remember you is never in our final answer. We're only doing that when we're doing u substitution and we have our solution.

Topics

Integrals

Integration

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Boston College

Lectures

Join Bootcamp