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受欢迎的微积分 >

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

解答

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

解答

10 sinh (x) + C

求解步骤

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

提出常数:

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

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

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

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

= 5 \cdot 2 sinh (u)

u = x

代回

= 5 \cdot 2 sinh (x)

化简

= 10 sinh (x)

解答补常数

= 10 sinh (x) + C

作图

流行的例子

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

limit as x approaches 4 of 7/(x-5)

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

limit as x approaches 0 of sin(pi/2-x)

derivative of log_{ln(x}(e))