integral of (cos(ln(4)x^2))/x

解

\int \frac{cos ( ln ( 4 ) x ^{2} )}{x} d x

\frac{1}{2} Ci (ln (4) x^{2}) + C

解答ステップ

\int \frac{cos ( ln ( 4 ) x ^{2} )}{x} d x

u置換積分法を適用する

= \int \frac{cos ( u )}{2 u} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{cos ( u )}{u} d u

非初等積分を使用する:

\int \frac{cos ( x )}{x} d x = Ci (x)

= \frac{1}{2} Ci (u)

代用を戻す

u = ln (4) x^{2}

= \frac{1}{2} Ci (ln (4) x^{2})

定数を解答に追加する

= \frac{1}{2} Ci (ln (4) x^{2}) + C