What is ∫ elogx + sinxcosxdx = 

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 Multiple Choice QuestionsMultiple Choice Questions

41.

What is dxx1 + lnxn equal to (n ≠ 1) ?

  • 1n - 11 + lnxn - 1 +c

  • 1 - n1 + lnx1 - n + c

  • n + 11 + lnx n + 1 + c

  • 1n - 11 + lnx n - 1 + c


42.

What is dx2x2 - 2x + 1 = ?

  • tan-12x - 12 +c

  • 2tan-12x - 1 +c

  • tan-12x + 12 +c

  • tan-12x - 1 + c


43.

What is the solution of the differential equation lndydx = x

  • y = ex  + c

  • y = e - x  + c

  • y = ln(x) + c

  • y = 2ln(x) + c


44.

What is the value of k such that integration of 3x2 + 8 - 4kx with respect to x, may be a rational function ?

  • 0

  • 1

  • 2

  • - 2


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45.

What is  dxxxn 1 = ?

  • 1nlnxnxn + 1 +c

  • lnxn + 1xn +c

  • lnxnxn + 1 +c

  • 1nlnxn + 1xn +c


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46.

What is  elogx + sinxcosxdx = ?

  • sinx + xcosx + sin2x2 + C

  • sinx - xcosx + sin2x2 + C

  • xsinx + cosx + sin2x2 + C

  • xsinx - cosx + sin2x2 + C


C.

xsinx + cosx + sin2x2 + C

Given that elogx + sinxcosxdx= x +sinxcosxdx= xcosx +sinxcosxdx=  xcosxdx + sinxcosxdx= xsinx + cosx . 1 + 22sinxcosxdx + c= xsinx + cosx + sin2x2dx +c=  xsinx + cosx + 12 - cos2x2 +c=  xsinx + cosx - cos2x4 + c=  xsinx + cosx - 1 - 2sin2x4 + c=   xsinx + cosx - 14 + 2sin2x4 +c=   xsinx + cosx + sin2x2 + c - 14=  xsinx + cosx + sin2x2 + C


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47.

What is the value of 0π4tan3x + tanxdx ?

  • 1414

  • 12

  • 1

  • 2


48.

If px = 4e2x, then what is pdx = ?

  • px1 + 2ln2 + c

  • px21 + 2ln2 + c

  • 2p1 + ln4 + c

  • px1 + ln2 + c


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