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Help me with 18th question please thankyou.............

Help me with 18th question please thankyou.............

Question Image
Grade:12

1 Answers

Aditya Gupta
2075 Points
3 years ago
let logx=y
the integral becomes
∫y*e^ydy/(1+y)^2=∫e^y(1/(1+y)-1/(1+y)^2)dy
we see that this is of the form e^x(f(x)+f’(x)), where f(x)=1/(1+x)
so the integral is
e^y/(1+y)
or x/(1+lnx) + C, where C is an arbitrary constant

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