integral of cot^2(x) Archives - Epsilonify Best solutions on internet! Fri, 15 Sep 2023 23:23:48 +0000 en-US hourly 1 https://wordpress.org/?v=6.4.5 https://www.epsilonify.com/wp-content/uploads/2022/09/cropped-E-M7-32x32.png integral of cot^2(x) Archives - Epsilonify 32 32 What is the integral of cot^2(x)? https://www.epsilonify.com/mathematics/calculus/what-is-the-integral-of-cot-square-x/ https://www.epsilonify.com/mathematics/calculus/what-is-the-integral-of-cot-square-x/#respond Tue, 24 Jan 2023 13:00:54 +0000 https://www.epsilonify.com/?p=1899 The integral of is . Proof. We want to determine the integral of : We have seen here that . So we get: Further, we saw here that the integral of is plus some constant. So, we get: Therefore, the integral of is .

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]]> \cot^2(x) is - x - \cot(x).

Proof. We want to determine the integral of \cot^2(x): 
\begin{align*}
\int \cot^2(x) dx.
\end{align*}
We have seen here that \cot^2(x) = \csc^2(x) - 1. So we get: 
\begin{align*}
\int \cot^2(x) dx &= \int (\csc^2(x) - 1)dx \\
&= \int \csc^2(x)dx - \int 1\cdot dx.
\end{align*}
Further, we saw here that the integral of \csc^2(x) is -\cot(x) plus some constant. So, we get: 
\begin{align*}
\int \cot^2(x) dx &= \int (\csc^2(x) - 1)dx \\
&= \int \csc^2(x)dx - \int 1\cdot dx \\
&= -\cot(x) - x + C.
\end{align*}
Therefore, the integral of \cot^2(x) is -\cot(x) - x.

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