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Problem 73 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^1_0 \frac{dx}{(1 + \sqrt{x})^4} $

Answer

$\frac{1}{6}$

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Video Transcript

we know that are you is one plus squirt of acts, which means that our two times you must one do you is equivalent to DX, which means the letters of integration are changed from 0 to 1 to one postcard of zero, which is one of the bottom toe one plus court of one, which is two on the top. Okay, now we're gonna be using the power rule to integrate, which means we increase the exponents by one. And then we divide by the new exponents using the fundamental damn of calculus. We can now pull again. We end up with 1/6 is our solution.