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$$$\sec^{2}{\left(\theta \right)}$$$の積分
入力内容
$$$\int \sec^{2}{\left(\theta \right)}\, d\theta$$$ を求めよ。
解答
$$$\sec^{2}{\left(\theta \right)}$$$ の不定積分は $$$\int{\sec^{2}{\left(\theta \right)} d \theta} = \tan{\left(\theta \right)}$$$ です:
$${\color{red}{\int{\sec^{2}{\left(\theta \right)} d \theta}}} = {\color{red}{\tan{\left(\theta \right)}}}$$
したがって、
$$\int{\sec^{2}{\left(\theta \right)} d \theta} = \tan{\left(\theta \right)}$$
積分定数を加える:
$$\int{\sec^{2}{\left(\theta \right)} d \theta} = \tan{\left(\theta \right)}+C$$
解答
$$$\int \sec^{2}{\left(\theta \right)}\, d\theta = \tan{\left(\theta \right)} + C$$$A
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