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人気のある微分積分 >

integral of (5cosh(sqrt(x)))/(sqrt(x))

解

\int \frac{5 cosh ( x )}{x} d x

解

10 sinh (x) + C

解答ステップ

\int \frac{5 cosh ( x )}{x} d x

定数を除く:

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

= 5 \cdot \int \frac{cosh ( x )}{x} d x

u置換積分法を適用する

= 5 \cdot \int 2 cosh (u) d u

定数を除く:

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

= 5 \cdot 2 \cdot \int cosh (u) d u

共通積分を使用する:

\int cosh (u) d u = sinh (u)

= 5 \cdot 2 sinh (u)

代用を戻す

u = x

= 5 \cdot 2 sinh (x)

簡素化

= 10 sinh (x)

定数を解答に追加する

= 10 sinh (x) + C

グラフ

人気の例

sum from n=0 to infinity of n/(2n^2+1)

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x \to 4 lim (\frac{7}{x - 5})

integral of (5x^2+7)/(x 4/3)

\int \frac{5 x ^{2} + 7}{x \frac{4}{3}} d x

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