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solve ∫(dx/(x(x n +1))

solve ∫(dx/(x(xn +1))

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
147 Points
12 years ago

Dear harshit agarwal

∫(dx/(x(xn +1))

multiply and devide by xn-1

integral will become

∫(xn-1dx/(xn(xn +1))

put xn=t

     nxn-1dx=dt

now integral will become

1/n∫(dt/(t(t +1))

=(1/n)∫(dt/[(t +1/2)2-(1/2)2]

this can be easly solve

by using the formula for

∫(dt/[(t)2-(a)2]

 


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Badiuddin


manoj jangra
8 Points
12 years ago

 just put

logx = y

1/xdx=dy

∫dy/eny  +1

from here you put take eny in numerator and put e-ny +1 = z

you will get answer  

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