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Numerade Educator



Problem 56 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{dx}{\sqrt{x} + x \sqrt{x}}\ $


$\int \frac{d x}{\sqrt{x}+x \sqrt{x}}=2 \tan ^{-1} \sqrt{x}+C$


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Video Transcript

for this. Let's use the substitution and then here differentiate and rewrite. This is let's say one over to you dx and then solve this for DX. You get to you. Do you here also notice you have X So you square this equation here that gives you x Yeah, So up top, There's RDX. So we have to you, Do you then here we have you and then there's X. And then here there's you again. So now let's go ahead and cancel off one of those use top and bottom and we're left only with one one. Plus, he's weird here. If you don't remember this, you could do a substitution. Triggs, Um, And when you use that, you should have to ten in verse pussy and then finally go back to your U sub to rewrite this is to our ten and then square. Relax and then add your C. And that's our answer