Evaluate the integral using the indicated substitution. \int\cot x \cos ec^{2}xdx,\ u=\cot x

Question

Evaluate the integral using the indicated substitution.

\int \cot x \cos e c^{2} x d x, u = \cot x

Answer 1

Consider the integrals,

\int \cot x \cdot \cos e c^{2} x \cdot d x

Let,

u = \cot x

d u = - \cos e c^{2} x d x

Substitute all value in given integrals,

\int \cot x \cdot \cos e c^{2} x \cdot d x = - \int u \cdot d u

= - \frac{u^{2}}{2} + C

= - \frac{1}{2} \cot^{2} x + C

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