Integration of (y*tan xy)

Question
Integrals
asked 2021-02-11
Integration of \(\displaystyle{\left({y}\cdot{\tan{{x}}}{y}\right)}\)

Answers (1)

2021-02-12
\(\displaystyle\int{y}{\tan{{x}}}{y}{\left.{d}{x}\right.}\)
\(\displaystyle\le{t}{u}={x}{y}\)
\(\displaystyle{d}\frac{{u}}{{\left.{d}{x}\right.}}={y}\)
\(\displaystyle{\left.{d}{x}\right.}={d}\frac{{u}}{{y}}\)
\(\displaystyle\int{y}{\tan{{x}}}{y}{\left.{d}{x}\right.}=\int{\left({y}{\tan{{u}}}\right)}{d}\frac{{u}}{{y}}\)
\(\displaystyle\int{\tan{{u}}}{d}{u}\)
\(\displaystyle={\ln{{\sec{{u}}}}}+{c}\)
\(\displaystyle\int{y}{\tan{{x}}}{y}{\left.{d}{x}\right.}={\ln{{\sec{{x}}}}}{y}+{c}\)
0

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