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intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb...

`intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e r ea , b in R^+)i se q u a lto` `1/(6lna^2b^3)a^(2x)b^(3x)ln(a^(2x)b^(3x))/e+k` `1/(6lna^2b^3)1/(a^(2x)b^(3x))ln1/(e a^(2x)b^(3x))+k` `1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k` `-1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k`

A

`(1)/(6lna^(2)b^(3))a^(2x)b^(3x)ln""(a^(2x)b^(3x))/(e)+k`

B

`(1)/(6lna^(2)b^(3))(1)/(a^(2x)b^(3x))ln""(1)/(ea^(2x)b^(3x))+k`

C

`(1)/(6lna^(2)b^(3))(1)/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k`

D

`-(1)/(6lna^(2)b^(3))(1)/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k`

Text Solution

Verified by Experts

The correct Answer is:
D
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FIITJEE-INDEFINTE INTEGRAL-ASSIGNMENT PROBLEMS (OBJECTIVE LEVEL-I)
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  2. If int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)Tan^(-1)((x^(2)+1)/(x)))=klog|tan...

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  3. If int\ x ln(1+1/x)\ dx = p(x)\ ln(1+1/x)+1/2 x - 1/2 ln(1+x) + c, c b...

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  4. int0^1T a n^(- 1)((2x)/(1-x^2))dx=

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  5. intsqrt(x)dx is equal to

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  6. If int((2x+1)dx)/(x^(4)+2x^(3)+x^(2)-1)=Aln|(x^(2)+x+1)/(x^(2)+x-1)|+C...

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  7. Let l(n)=int(0)^(1){P(x^(2))+P(x^(2)-1)}^(n)dx. If (k+1)l(n)=2k(1+l(n-...

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

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  9. Evaluate: int(x^2-1)/((x^4+3x^2+1)tan^(-1)(x+1/x))dx

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  10. int(cos2theta)/((sintheta+costheta)^(2))d""theta is equal to

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  11. int ((x+2)/(x+4))^2 e^x dx is equal to

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  12. int e^(x^4) (x + x^3 +2x^5) e^(x^2) dx is equal to

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  13. 4 int (sqrt(a^(6)+x^(8)))/(x) dx is equal to

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  14. intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e...

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  15. The value of int(1+sin2theta)/(sintheta-costheta)d""theta is equal to

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  16. int((sin2x)^(1//3)d(root(3)(tanx)))/(sin^(2//3)x+cos^(2//3)x) is equal...

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  17. int (dx)/(x^(2)(x^(4)+1))is

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  18. inttan^(-1)alpha,tanxdalpha equals

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  19. intdx/[{(x-5)+(x-7)}sqrt((x-5)(x-7))]

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  20. Statement-1: A function is given by g(x)=ln""(x^(2)+1)/(x^(2)-1) becau...

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