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受欢迎的微积分 >

integral of cos^4(7-x)sin(7-x)

解答

\int cos^{4} (7 - x) sin (7 - x) d x

解答

\frac{1}{5} cos^{5} (7 - x) + C

求解步骤

\int cos^{4} (7 - x) sin (7 - x) d x

使用换元积分法

= \int - cos^{4} (u) sin (u) d u

提出常数:

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

= - \int cos^{4} (u) sin (u) d u

使用换元积分法

= - \int - v^{4} d v

提出常数:

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

= - (- \int v^{4} d v)

使用幂法则

= - (- \frac{v ^{5}}{5})

代回

= - (- \frac{cos ^{5} ( 7 - x )}{5})

化简

- (- \frac{cos ^{5} ( 7 - x )}{5}) : \frac{1}{5} cos^{5} (7 - x)

= \frac{1}{5} cos^{5} (7 - x)

解答补常数

= \frac{1}{5} cos^{5} (7 - x) + C

作图

流行的例子

(dy)/(dx)=e^{3y}sin(4x)

\frac{d y}{d x} = e^{3 y} sin (4 x)

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

n = 0 \sum \infty \frac{1}{n ^{2} + 2 n}

integral of (5000x)/(25x+1500)

\int \frac{5000 x}{25 x + 1500} d x

limit as x approaches 0 of 1/(4x)

x \to 0 lim (\frac{1}{4 x})

derivative of cos(2x+5)

\frac{d}{d x} (cos (2 x + 5))