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Quick Question - Integration

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Quick Question - Integration

emmaxoxo

I'm trying to integrate

\int \frac{x}{(x-1)^{\frac{1}{2}}} dx

So I said Let

u=x-1

x=u+1

and

\frac{du}{dx}=1 \rightarrow du=dx

Therefore

\int \frac{u+1}{u^{\frac{1}{2}}} dx \rightarrow \int (u^\frac{1}{2}+ u^{-\frac{1}{2}}) dx \rightarrow \frac{2}{3}u^{\frac{3}{2}}+ 2u^{\frac{1}{2}} +C

Then when subbing u back in

\frac{2}{3}(x-1)^{\frac{3}{2}}+2\sqrt{x-1}+C

Whereas the answer is suppose to be

\frac{2}{3}(x+2)\sqrt{x-1} +C

What am I doing wrong?

Reply 1

DFranklin

Take out the common factor of

\sqrt{x-1}

in your answer, you should end up with what the book says.

DFranklin

Take out the common factor of

\sqrt{x-1}

in your answer, you should end up with what the book says.

Thanks Got it!

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