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Evaluate the following integral ∫1/x(x^5+3) dx
Q:

Evaluate the following integral ∫1/x(x^5+3) dx

hamza
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2022-05-18
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Evaluate the following integral ∫1/x(x^5+3)   dx

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hamza
2022-05-18
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Put     1/z=x^5      
 so    x=z^(-1/5)      and     dx=-1/5 z^(-6/5)  dz
∫1/(z^(-1/5) (1/z+3) )-1/5 z^(-6/5)  dz=-1/5 ∫z^(-6/5)  dz
I=(-1)/15  ln⁡|1+3z|=(-1)/15  ln⁡|1+3x^(-5) |+c

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