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If int f(x)dx=psi(x), then int x^5f(x^3)...

If `int f(x)dx=psi(x)`, then `int x^5f(x^3)dx`

A

`(1)/(3)x^(3)Psi(x)^(3)-3intx^(3)Psi(x^(3))dx+C`

B

`(1)/(3)x^(3)Psi(x^(3))-intx^(2)Psi(x^(3))dx+C`

C

`(1)/(3)[x^(3)Psi(x^(3))-[x^(3)Psi(x^(3))dx]+C`

D

`(1)/(3)[x^(3)Psi(x^(3))-intx^(2)Psi(x^(3))dx]+C`

Text Solution

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-INDEFINITE INTEGRATION-QUESTION FROM PREVIOUS YEARS.AIEEE/JEE MAIN PAPERS
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  2. int(dx)/(x+x^7)=p(x), then int x^6/(x+x^7) dx is

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  3. If int f(x)dx=psi(x), then int x^5f(x^3)dx

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

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  5. int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=

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  6. The integral intxcos^(-1)((1-x^(2))/(1+x^(2)))dx(xgt0) is equal to

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  7. int ((sin^2xcos^2x)/(sin^3x+cos^3x))dx=

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  8. If m is a non-zero number and int (x^(5m-1)+2x^(4m-1))/(x^(2m)+x^m+1)^...

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  9. The integral int(dx)/(x^(2)(x^(4)+1)^(3//4)) equal

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  10. The integral I = int (dx)/((x+1)^(3//4)(x-2)^(5//4)) is equal to

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  11. if I=int(log(t+sqrt(1+t^2)))/sqrt(1+t^2)dt=1/2(g(t))^2+c then g(2) is ...

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  12. The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to ...

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  13. The integral int(1)/((1+sqrt(x))sqrt(x-x^(2)))dx is equal to (where C ...

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  14. If int(1)/(cos^(2)xsqrt(2 sin2x))dx=(tanx)^(A)+C(tanx)^(B)+k, where k...

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  15. Evaluate: intsqrt(1+2cotx(cotx+cosecx))dx

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  16. I ff((3x-4)/(3x+4))=x+2, x!=4/3,andintf(x)dx=Alog|1-x|+B x+C then orde...

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  17. Let In=int tan^n x dx, (n>1). If I4+I6=a tan^5 x + bx^5 + C, Where C...

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  18. If int (2x + 5 )/(sqrt(7 - 6 x - x ^ 2 )) dx = A sqrt (7 - ...

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  19. if f ((x- 4 ) /(x + 2 )) = 2 x + 1 , (x in R - { 1, - 2 }) , ...

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  20. int\ (sin^2 x cos^2x)/(sin^5x+cos^3xsin^2x+sin^3xcos^2x+cos^5x)^2 \ d...

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