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```
Find ∫f(x)dx If, f[(3x-4)/3x+4)] = x+2

```
9 years ago 419 Points
```							Dear Shreyans
first calculate f(x)
put 3x-4/3x+4 = y
calculate x in terms of y
x=4(1+y)/3(1-y)
x+2=2(5-y)/3(1-y) = 2(y-5)/3(y-1)
f(y)=2(y-5)/3(y-1)
f(x)=2(x-5)/3(x-1)
to integrate this use partial fractions
f(x)=2/3 [(x-1-4)/(x-1)]= 2/3[1 - 4/x-1]
now integration is simple
∫2/3[1 - 4/x-1]dx
2/3[x-4log(x-1)] + C

All the best.
AKASH GOYAL

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```
9 years ago
```							put 3x-4/3x+4=t,
on solving by componendo and dividendo,
6x/-8=t+1/t-1
x=4(t+1)/3(1-t)
put this in the given condition, get f(x), then integrate it
```
9 years ago 605 Points
```							Dear student,Please fidn the solution to your problem. first calculate f(x)put 3x-4/3x+4 = ycalculate x in terms of yx=4(1+y)/3(1-y)x+2=2(5-y)/3(1-y) = 2(y-5)/3(y-1)f(y)=2(y-5)/3(y-1)f(x)=2(x-5)/3(x-1)to integrate this use partial fractionsf(x)=2/3 [(x-1-4)/(x-1)]= 2/3[1 - 4/x-1]now integration is simple∫2/3[1 - 4/x-1]dx= 2/3[x-4log(x-1)] + C Thanks and regards,Kushagra
```
3 months ago
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