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int(1+x-x^(-1))e ^(x+x^(-1))dx=...

`int(1+x-x^(-1))e ^(x+x^(-1))dx=`

A

`(x+1)e^(x+x^(-1))+C`

B

`(x-1)e^(x+x^(-1))+C`

C

`-xe^(x+x^(-1))+C`

D

`xe^(x+x^(-1))+C`

Text Solution

Verified by Experts

The correct Answer is:
d
Let `I=int(1+x-x^(-1))e^(x+x^(-1))dx`
`rArrI=inte^(x+x^(-1))dx+intx(1-(1)/(x^(2)))e^(x+x^(-1))dx`
`rArr I=inte^(x+x^(-1))dx+intunderset(I)(x)e^(x+x^(-1))d(x+x^(-1))`
`rArr I=inte^(x+x^(-1))dx+xe^(x+x^(-1))-inte^(x+x^(-1))dx`
`rArrI=xe^(x+x^(-1))+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
  1. intdx/((2x-7)sqrt(x^2-7x+12) is equal to

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  2. The value of int x log x (log x - 1) dx is equal to

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  3. int(1+x-x^(-1))e ^(x+x^(-1))dx=

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  4. If I(n)=int("In "x)^(n)dx, " then " I(n)+nI(n-1)=

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  5. The value of int(sin^(2)xcos^(2)x)/((sin^(3)x+cos^(3)x)^(2))dx , is

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  6. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

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  7. If f(x) = int ((x^(2) + sin ^(2)x))/(1+x^(2))sec^(2) x dx and f(0) = ...

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  8. At present, a firm is manufacturing 2000 items. It is estimated tha...

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  9. "If " int f(x)dx=Psi(x), " then " int x^(5)f(x)^(3)dx " is equal to "

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  10. "The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "

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  11. if int(1-5sin^2x)/(cos^5xsin^2x)dx=f(x)/(cos^5x)+c then f(x)

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  12. int(x^(7m)+x^(2m)+x^m)(2x^(6m)+7x^m+14)^(1/m)dx

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  13. int (x dx)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))) is equal to

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  14. intsqrt(x-3)(sin^(-1)(Inx)+cos^(-1)(Inx))dx is equal to

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  15. "The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "

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  16. inte^(x^(4))(x+x^(3)+2x^(5))e^(x^(2))dx is equal to

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  17. int(sin(101x).sin^(99)x)dx equals

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  18. Suppose int(1-7cos^2x)/(sin^7xcos^2x)dx=(g(x))/(sin^7x)+c where C is a...

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  19. int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx is equal to

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  20. If int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ dx = lambda ((2+x)/(2-x))^mu + ...

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