# Integration of (y*tan xy)

Question
Integrals
Integration of $$\displaystyle{\left({y}\cdot{\tan{{x}}}{y}\right)}$$

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

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