integral of cosh(3x)

解答

\int cosh (3 x) d x

\frac{1}{3} sinh (3 x) + C

求解步骤

\int cosh (3 x) d x

使用换元积分法

= \int cosh (u) \frac{1}{3} d u

提出常数:

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

= \frac{1}{3} \cdot \int cosh (u) d u

使用积分常见定则:

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

= \frac{1}{3} sinh (u)

u = 3 x

代回

= \frac{1}{3} sinh (3 x)

解答补常数

= \frac{1}{3} sinh (3 x) + C

x \frac{d y}{d x} - y = x^{2} - y^{2}

\int sin^{3} (x) cos^{\frac{3}{2}} (x) d x

x \frac{d y}{d x} - 3 y = x y^{4}

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