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intx logx dx is equal to...

`intx logx dx` is equal to

A

`(x^2)/(4)(2logx-1)+C`

B

`(x^2)/(2)(2logx-1)+C`

C

`(x^2)/(4)(2logx+1)+C`

D

`(x^2)/(2)(2logx+1)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`int overset(II)(x)logx dx =logx.(x^2)/(2)-int(1)/(x).(x^2)/(2)dx`
`=(x^2)/(2)log x-(1)/(2)(x^2)/(2)+C`
`=(x^2)/(4)(2log x-1)+C`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 02-Paper 2 (Mathematics )
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  2. For the function f(x)=xe^x, the point

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  3. intx logx dx is equal to

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  4. A die is thrown 100 times. Getting an even number is considered a...

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  5. The angle between the line (x-3)/(2)=(y-1)/(1)=(z+4)/(-2) and the plan...

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  6. If in a triangle ABC, 3 sin A = 6 sin B=2sqrt3sin C, then the angle A...

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  7. The differential equation of all circles which passes through the orig...

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  8. The value of the integral int (0)^(pi//2)(sin^100x-cos^100x)dx is

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  9. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

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  10. If 2a+3b+6c=0, then prove that at least one root of the equation a x^2...

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  11. int(sin^(-1)x)/(sqrt(1-x^(2)))dx is equal to Where, C is an arbitra...

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  12. If X and Y are independent binomial vatiates B(5,1/2) and B(7,1/2) and...

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  13. sin((1)/(2)cos^(-1).(4)/(5)) is equal to

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  14. In a Delta ABC , if A,B,C are in AP, then (a)/(c) sin2C+(c)/(a)(sin2A)...

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  15. The general solution of the differential equation (dy)/(dx)+(1+cos2y)/...

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  16. The number of values of x in the interval [0,5pi] satisfying the equat...

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  17. Let A(1,-1,2) and B(2,3-1) be two points. If a point P divides AB inte...

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  18. If the line y cos alpha = x sin alpha +a cos alpha be a tangent to t...

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  19. The value of lambda for which the curve (7x + 5)^2 + (7y + 3)^2 = lam...

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  20. if y=4x+3 is parallel to a tangent to the parabola y^2=12x, then its d...

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