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)/(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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