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Problem 63 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^{13}_0 \frac{dx}{\sqrt[3]{(1 + 2x)^2}} $

Answer

$$3$$

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Video Transcript

Okay, We're gonna say you is gonna be what's under the square root, which is one plus two acts. Which means our D axe is gonna be 1/2 to you. Or do you divide by two. Which means the limits of integration not changed rooms the other 13 to 1 plus two times zero, which is one one post, two times 13 which is 27 times 1/2. Do you okay? Pull out the constant 1/2. Okay, We're now gonna be evaluating integral using the power rule, which means we're gonna be increasing the exploited by one toe, 1/3 dividing by the new exponents. They using the fundamental dilemma Kokkalis plugging the bounds and we end up with three is our solution.