$$$\tan{\left(t \right)} \sec{\left(t \right)}$$$の積分
関連する計算機: 定積分・広義積分計算機
入力内容
$$$\int \tan{\left(t \right)} \sec{\left(t \right)}\, dt$$$ を求めよ。
解答
$$$\tan{\left(t \right)} \sec{\left(t \right)}$$$ の不定積分は $$$\int{\tan{\left(t \right)} \sec{\left(t \right)} d t} = \sec{\left(t \right)}$$$ です:
$${\color{red}{\int{\tan{\left(t \right)} \sec{\left(t \right)} d t}}} = {\color{red}{\sec{\left(t \right)}}}$$
したがって、
$$\int{\tan{\left(t \right)} \sec{\left(t \right)} d t} = \sec{\left(t \right)}$$
積分定数を加える:
$$\int{\tan{\left(t \right)} \sec{\left(t \right)} d t} = \sec{\left(t \right)}+C$$
解答
$$$\int \tan{\left(t \right)} \sec{\left(t \right)}\, dt = \sec{\left(t \right)} + C$$$A
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