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Integrate the functions xsqrt(1+2x^2)...

Integrate the functions `xsqrt(1+2x^2)`

Text Solution

Verified by Experts

Let us take `1+2x^2=t`
=`4xdx=dt`
⇒`∫xsqrt(1+2x^2) ​dx`
=`∫(sqrt(t))/4*dt`
=`1/4*​∫t^(1/2)​dt`
=`1/4​((t)^(3/2)​​)/(3/2)+C`
=`1/6*​(1+2x^2)^(3/2)​+C`
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