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int((x+2)/(x+4))^2 e^xdx is equal to...

`int((x+2)/(x+4))^2 e^xdx` is equal to

A

`e^(x)((x)/(x+4))+c`

B

`e^(x)((x+2)/(x+4))+c`

C

`e^(x)((x-2)/(x+4))+c`

D

`((2x e^(2))/(x+4))+c`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int((x+2)/(x+4))^(2)e^(x) dx=int e^(x)[(x^(2)+4x+4)/((x+4)^(2))]dx`
`=int e^(x)[(x(x+4))/((x+4)^(2))+(4)/((x+4)^(2))]dx`
`=int e^(x)[(x)/(x+4)+(4)/((x+4)^(2))]dx`
`=e^(x) ((x)/(x+4))+C`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  14. int e^(sin^(-1)x)((log(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

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  15. If xf(x)=3f^2(x)+2,t h e nint(2x^2-12 xf(x)+f(x))/((6f(x)-x)(x^2-f(x)...

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  19. 4int(sqrt(a^6+x^8))/x dx is equal to (a)sqrt(a^6+x^8)+(a^3)/2ln|...

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