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Question

Integrate the following functions.
x+2x21dx.

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Solution

x+2x21dx=xx21dx+2x21dx=I1+I2....(i)
Now, I1=xx21dx,
Let x21=t2xdx=dtdx=dt2x
I1=xt×dt2x=12dtt=12t12dt=12[2t12]=t=x21+C2(t=x21)
Now, I2=21x21dx=2log|x+x21|+C1[dxx2a2=log|x+x2a2|]
On putting the values of I1 and I2 in Eq. (i), we get
I=x21+2log|x+x21|+C
where, C=C1+C2


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