Integral Calculus> Integration of 7+logx/(8+logx)^2 .dx plea...

Integration of 7+logx/(8+logx)^2 .dx please get me the ans as quick as possible

Keyur , 7 Years ago

Grade 12

3 Answers

Nandana

Last Activity: 7 Years ago

hi ,

while doing I troubled to get the integration of e^x / x , if you know this please inform me

I’ll try to get the answer … !

Sanket

Last Activity: 7 Years ago

$\int (7+log x)/(8+logx)^{2}$

substutute x=e^t

dx = e^tdt

this gives

$\int (7+t)/(8+t)^2 e^tdt$

$=\int e^t [1/(8+t)-1/(8+t)^2]$

and /int e^x {f(x) + f’(x)} . dx = f(x)e^x

so, we get e^t/(8+t)

then replace t = log x to get final answer

Nandana

Last Activity: 7 Years ago

Hi... For this question integrate ∫(7+logx/(8+logx)^2 .dx ) = ∫(7+1-1+log x)/(8+log x)^2 = ∫1/(8+log x) dx -∫1/(8+log x)^2 dx By using integration by parts u = 1/(8+log x ) ; dv = dx du = -1/(8+log x)*1/x ; v = x For the 1st part ∫1/(8+log x) dx = ×/(8+logx) +∫1/(8+log x)^2 dx Finally ,= ×/(8+logx) +∫1/(8+log x)^2 dx -∫1/(8+log x)^2 dx =x /(8+ log x) + K Thank you