Question

Please refer the image and provide solution​

Answer 1

Answer:

x / ( 6 + logx ) + C

Step-by-step explanation:

To find ----> ∫ ( 5 + logx ) / ( 6 + logx )² dx

Solution -----> 1) Plz see the attachment

2) First we add and subtract 1 in numerator .

3) Then we break given integral in to two integrals .

4) Then we integrate first integral by integration by parts . Formula of integration by parts is ,

∫ u v dx = u ∫ v dx - ∫ { d/dx ( u ) ∫ v dx } dx

5) In given question we suppose

u = 1 / ( 6 + logx ) and v = 1

and applied above formula of integration by parts by using some formulee

1) d/ dx ( 1 / x ) = - 1 / x²

2) d / dx ( logx ) = 1 /x

3) ∫ 1 dx = x

Applying these formulee , we get, the answer.

Additional information ----->

1) We must know how we choose u and v in integration by parts , we have a word

I L A T E

I = Inverse function

L = Log function

A = Algebric function

T = Trigonometric function

E = Exponential function

Which function is appear first in this word we suppose it u and other function is treated as v .