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
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
B.
Given that px =4e2xIntegrating both sides ∫pxdx =∫4e2xdx ∫pxdx = ∫42xe2xdx ∫pxdx = 42x∫e2xdx - ∫ddx42x∫e2xdxdx + c ∫pxdx = 42xe2x2 - ∫42x . 2 . ln4 . e2x2dx + c ∫pxdx = px2 - ln4∫pxdx + c ∫pxdx + ln4∫pxdx = px2 + c ∫pxdx1 + ln4 = px2 + c ∫pxdx = px21 + ln4 + c