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int e^x {f(x)-f'(x)}dx= phi(x), then int...

`int e^x {f(x)-f'(x)}dx= phi(x)`, then `int e^x f(x) dx` is

A

`phi(x)=e^(x)f(x)`

B

`phi(x)-e^(x)f(x)`

C

`(1)/(2){phi(x)+e^(x)f(x)}`

D

`(1)/(2){phi(x)+e^(x)f'(x)}`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `int e^(x){f(x)-f'(x)}dx=phi(x)`
and `int e^(x){f(x)+f'(x)}dx=e^(x)f(x)`
On adding, we get `2int e^(x)f(x)dx=phi(x)+e^(x)f(x)`
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CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
  1. The integral int(2x^(12)+5x^9)/((x^5+x^3+1)^3)dx is equal to:

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  2. If In=int( lnx)^n dx then In+nI(n-1)

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  3. int e^x {f(x)-f'(x)}dx= phi(x), then int e^x f(x) dx is

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  4. For x >1,int sin^(- 1)((2x)/(1+x^2))dx is equal to

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  5. If int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)) dx=asqrt(1+x^2)ln(x+sqrt(1+x...

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  6. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

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  7. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

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  8. "If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

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  9. int x sinx sec^(3)x dx is equal to

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  10. int e^(tan^-1x)(1+x+x^2) d(cot^-1x) is equal to

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  11. int e^(x)((2 tanx)/(1+tanx)+cot^(2)(x+(pi)/(4)))dx is equal to

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  12. int e^(x^4) (x + x^3 +2x^5) e^(x^2) dx is equal to

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  13. The value of integral inte^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))dxi s...

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  14. int e^(x)((x^(2)+1))/((x+1)^(2))dx is equal to

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

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  16. inte^(tanx)(sinx-secx)dx is equal to

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  17. int(cosec^2x-2005)/cos^[2005]x.dx

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  18. int(1+2x^(2)+(1)/(x))e^(x^(2)+(1)/(x))dx is equal to

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  19. int e^(sin^(-1)x)((log(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

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  20. Ifxf(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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