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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-1`

B

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

C

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

D

`f(x)=2(x+2)`

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The correct Answer is:
d
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Chapter Test
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  2. "If " int xlog(1+1//x)dx=f(x)log(x+1)+g(x)x^(2)+Ax+C, then

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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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  6. If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C, then

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

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  10. Let f(x)=(x)/((1+x^(n))^(1//n)) for n ge 2 and g(x)=underset("n times"...

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  11. The value of int ((ax^(2)-b)dx)/(xsqrt(c^(2)x^(2)-(ax^(2)+b)^(2))) is ...

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  12. Evalaute: inte^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n))dx

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  13. int(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx

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

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  16. What is int (x^(2) +1)/(x^(4) - x^(2) + 1) dx equal to ?

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  17. Evaluate: int(x-1)/((x+1)sqrt(x^3+x^2+x))dx

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  18. int(1+x^(2))/(xsqrt(1+x^(4)))dx is equal to

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  19. int(1+x^(4))/((1-x^(4))^(3//2))dx is equal to

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  20. If int(dx)/(x^(4)+x^(3))= A/x^(2)+B/x+ln|x/(x+1)|+C, then

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