negative cotangent -- dcot(x)/dx=-csc^2(x)
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Using u-substitution (where u = sinx), you'll find the antiderivative to be 0.5*sin2x + C.
No. The inverse of the secant is called the arc-secant. The relation between the secant and the cosecant is similar to the relation between the sine and the cosine - they are somehow related, but they are not inverse functions. The secant is the reciprocal of the cosine (sec x = 1 / cos x). The cosecant is the reciprocal of the sine (cos x = 1 / sin x).
X(logX-1) + C
Reciprocal of Cosine is Secant
(2/3)*x^(3/2)