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The value of the integral int(xsinx^(2)e...

The value of the integral `int(xsinx^(2)e^(secx^(2)))/(cos^(2)x^(2))dx` , is

A

`(1)/(2)e^(secx^(2))+C`

B

`(1)/(2)e^(sinx^(2))+C`

C

`(1)/(2)sinx^(2)e^(cos^(2)x^(2))+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Let `I=int(xsinx^(2)e^(secx^(2)))/(cos^(2)x^(2))dx=(1)/(2)inte^(secx^(2)).2xtanx^(2)secx^(2)dx`
`I=(1)/(2)e^(secx^(2))d(secx^(2))=(1)/(2)e^(secx^(2))+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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  2. int(e^((x^(2)+4Inx))-x^(3)e^(x^(2)))/(x-1)dx equals to

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  3. The value of the integral int(xsinx^(2)e^(secx^(2)))/(cos^(2)x^(2))dx ...

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  4. int(1)/((x-1)sqrt(x^(2)-1))dx equals

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  6. int(1-x^(7))/(x(1+x^(7)))dx equals

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  7. Evaluate: (sin^3x dx)/((cos^4x+3cos^2x+1)tan^(-1)(secx+cosx)

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  8. int((x-x^5)^(1//5))/(x^6)dx is equal to :

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  9. int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx is equal to

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  10. If intsqrt((cos^(3)x)/(sin^(11)x))dx =-2(Atan^(-9/2)+Btan^(-5/2)x) + C...

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  11. int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x...

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  12. int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x...

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  14. Let the equation of a curve passing through the point (0,1) be given b...

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  15. Evaluate: int1/(sin^4x+cos^4x)dx

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  16. Evaluate the following Integrals : int (sec x .dx)/(sqrt(sin (x+2A...

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  18. Evaluate "if " int(1)/(x+x^(5))dx=f(x)+c," then " int(x^(4))/(x+x^(5...

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  19. If intf(x)dx=F(x), then int x^(3)f(x^(2))dx is equal to

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  20. If n is an odd positive integer, then int|x^(n)|dx is equal to

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