(1/4)x^2(2logx-1) + c
Using chain rule:integral of cos2x dx= 1/2 * sin2x + C
There are a lot of rules for integration! Plus a lot of techniques! Here is the power rule as a simple example. int[Xn dx] = (Xn + 1)/(n + 1) + C ( n does not equal - 1 )
âˆ« (1/x) dx = ln(x) + C C is the constant of integration.
âˆ« xn dx = xn+1/(n+1) + C (n â‰ -1) C is the constant of integration.
Integral( sin(2x)dx) = -(cos(2x)/2) + C
integral x/(x-1) .dx = x - ln(x-1) + c where ln = natural logarithm and c = constant of integration alternatively if you meant: integral x/x - 1 .dx = c
âˆ« 1/cos2(x) dx = tan(x) + C C is the constant of integration.
âˆ« 1/sinh2(x) dx = -cotanh + C C is the constant of integration.
This is a trigonometric integration using trig identities. S tanX^3 secX dX S tanX^2 secX tanX dX S (secX^2 -1) secX tanX dX u = secX du = secX tanX S ( u^2 - 1) du 1/3secX^3 - secX + C