原始関数一覧(基礎編)

$$
\begin{array}{}
\displaystyle
\int{}x^a\,dx&=&\dfrac{1}{a+1}x^{a+1}   (a≠-1)\\\\
\displaystyle
\int{}\dfrac{dx}{x}&=&\log|x|\\\\
\displaystyle\int{}\sin{}x\,dx&=&-\cos{}x\\\\
\displaystyle\int{}\cos{}x\,dx&=&\sin{}x\\\\
\displaystyle\int{}\tan{}x\,dx&=&-\log|\cos{}x|\\\\
\displaystyle\int{}e^x\,dx&=&e^x\\\\
\displaystyle\int{}\log{}x\,dx&=&x\log{}x-x\\\\
\end{array}
$$

$$
\begin{array}{}
\displaystyle\int{}\arcsin{}x\,dx
&=&x\arcsin{}x+\sqrt{1-x^2}\\\\
\displaystyle\int{}\arctan{}x\,dx
&=&x\arctan{}x-\dfrac{1}{2}\log\left(1+x^2\right)\\\\
\displaystyle\int{}\frac{dx}{\sqrt{1-x^2}}
&=&\arcsin{}x\\\\
\displaystyle\int{}\frac{dx}{1+x^2}
&=&\arctan{}x\\\\
\displaystyle\int{}\frac{dx}{\sin{}x}
&=&\dfrac{1}{2}\log\dfrac{1-\cos{}x}{1+\cos{}x}\\\\
\displaystyle\int{}\frac{dx}{\cos{}x}
&=&\dfrac{1}{2}\log\dfrac{1+\sin{}x}{1-\sin{}x}\\\\
\displaystyle\int{}\frac{dx}{\tan{}x}&=&\log|\sin{}x|
\end{array}
$$