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

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

A

`(1)/(6Ina^(2)b^(3))a^(2x)b^(3x)In(a^(2x)b^(3x))/(e)+k`

B

`(1)/(6Ina^(2)b^(3))(1)/(a^(2x)b^(3x))In(1)/(ea^(2x)b^(3x))+k`

C

`(1)/(6Ina^(2)b^(3))(1)/(a^(2x)b^(3x))In(a^(2x)b^(3x))+k`

D

`-(1)/(6Ina^(2)b^(3))(1)/(a^(2x)b^(3x))In(a^(2x)b^(3x))+k`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int x((Ina^(a^(x//2)))/(3a^(5x//2)b^(3x))+(Inb^(b^(x)))/(2a^(2x)b^(4x)))dx=int(Ina^(2x)b^(3x))/(6a^(2x)b^(3x))dx `
` "Let " a^(2x)b^(3x)=t. " Then " tIna^(2)b^(3)dx=dt.`
`"Therefore, " I=int(1)/(6Ina^(2)b^(3))(Int)/(t^(2))dt`
`=(1)/(6Ina^(2)b^(3))((-Int)/(t)-int(-1)/(t^(2))dt)`
`=-(1)/(6Ina^(2)b^(3))((In et)/(t))+k`
`=-(1)/(6Ina^(2)b^(3))((Ina^(2x)b^(3x)e)/(a^(2x)b^(3x)))+k`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  2. int sqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to

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

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  4. int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c ...

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  5. "If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))...

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  6. The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...

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  7. If int(dx)/(sqrt(sin^3xcos^5x))=asqrt(cotx)+bsqrt(tan^3)x+c , then a=-...

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  8. Ifint(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c ,t h e n a=(sq...

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  9. Evaluate: int dx/( (x + 2)(x^2 + 1) )

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  10. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

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  11. If intf(x)sinxcosxdx=1/(2(b^2-a^2))lnf(x)+c ,then f(x) is equal to

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  12. int(x^(5))/((4x^(2)+ 1)^(4))dx is equal to

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  13. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h...

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  14. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

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  15. int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3...

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  16. If I=int (dx)/((a^(2)-b^(2)x^(2))^(3//2)), then I equals

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  17. int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a) sqrt(x^2+1/(x^2)+1)+C (b) (...

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  18. int(sqrt(x^2+1))/(x^4)dx=

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  19. int (1+2x^(6))/((1-x^(6))^(3//2))dx is equal to

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  20. The integral int[2x^[12]+5x^9]/[x^5+x^3+1]^3.dx is equal to-

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