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
What is ∫dx2x2 - 2x + 1 = ?
tan-12x - 12 + c
2tan-12x - 1 + c
tan-12x + 12 + c
tan-12x - 1 + c
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
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
What is ∫ dxxxn 1 = ?
1nlnxnxn + 1 + c
lnxn + 1xn + c
lnxnxn + 1 + c
1nlnxn + 1xn + c
What is ∫ elogx + sinxcosxdx = ?
sinx + xcosx + sin2x2 + C
sinx - xcosx + sin2x2 + C
xsinx + cosx + sin2x2 + C
xsinx - cosx + sin2x2 + C
C.
Given that ∫elogx + sinxcosxdx= ∫x + sinxcosxdx= ∫xcosx + sinxcosxdx= ∫xcosxdx + ∫ sinxcosxdx= xsinx + cosx . 1 + ∫22 sinxcosxdx + 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
What is the value of ∫0π4tan3x + tanxdx ?
1414
12
If px = 4e2x, then what is ∫pdx = ?
px1 + 2ln2 + c
px21 + 2ln2 + c
2p1 + ln4 + c
px1 + ln2 + c