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If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqr...

If `int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C`, then

A

`f(x) = x - 2, g(x) = (sqrt(1-e^(x))-1)/(sqrt(1+e^(x)) + 1)`

B

`12(((1+root(4)(x))^(7//3))/(7)-((1+root(4)(x))^(4//3))/(4))+c`

C

`6(((1+root(4)(x))^(7//3))/(7)-((1+root(4)(x))^(4//3))/(4))+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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VMC MODULES ENGLISH-INTEGRAL CALCULUS-1-LEVEL 1
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  2. If int ( dx )/(5 + 4 sin x) = A tan^(-1) ( B tan ((x)/(2)) + (4)/(3))...

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  3. If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C, then

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  4. If int (dx)/(5+4 cos x) = k tan^(-1) (m tan ((x)/(2))) + C then :

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  5. int (1)/((x+5)sqrt(x+4))dx is :

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  6. Evaluate: inte^x\ [(secx+log(secx+tanx)]\ dx

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  7. If int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=aln((x-1)/(x+1))+btan^(-1).(x)...

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  8. int \ 1/x{loge^(e x)*loge^(e^2x) * loge^(e^3x)}dx

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  9. Evaluate: inte^x\ (tanx-logcosx)\ dx

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  10. If int(1)/((sinx+4)(sinx-1))dx =A(1)/("tan"(x)/(2)-1)+B"tan"^(-1){f(...

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  11. The value of int [f(x)g''(x) - f''(x)g(x)] dx is equal to

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  12. If int[sin^2x]/[1+sin^2x] dx =x-ktan^-1(M tanx) then: a. M=1/sqrt2 b....

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  13. If f(x) = (1)/(cos^2xsqrt(1-tan x)) then its anti-derivative F(x) sati...

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  14. If f(x) =(1)/(cos^(2)xsqrt(1+tanx)), then its anit-derivate F(x) s...

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  15. Let f(x)=1/(4-3cos^2x+5sin^2x) and if its antiderivative F(x)=(1/3) ta...

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  16. The value of int frac{dx}{x^2+5x+6} is:

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  17. If polynomials P and Q satisfyint[(3x-1)cosx+(1-2x)sinx ]dx=P cosx+Qsi...

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  18. Evaluate: int(sin^2x)/(cos^6x)\ dx

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  19. If int frac{3cosx+2sinx}{4sinx+5cosx}dx=Ax+Blog|4sinx+5cosx|+C,then:

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  20. If int frac{xdx}{x^2-4x+8}=K log (x^2-4x+8)+tan^(-1)(frac{x-2}{2})+C, ...

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