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受欢迎的微积分 >

integral of 5cos^2(x)sin(2x)

解答

\int 5 cos^{2} (x) sin (2 x) d x

解答

- \frac{5}{2} cos^{4} (x) + C

求解步骤

\int 5 cos^{2} (x) sin (2 x) d x

提出常数:

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

= 5 \cdot \int cos^{2} (x) sin (2 x) d x

使用换元积分法

= 5 \cdot \int - u d u

提出常数:

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

= 5 (- \int u d u)

使用幂法则

= 5 (- \frac{u ^{2}}{2})

u = cos^{2} (x)

代回

= 5 (- \frac{( cos ^{2} ( x ) ) ^{2}}{2})

化简

5 (- \frac{( cos ^{2} ( x ) ) ^{2}}{2}) : - \frac{5}{2} cos^{4} (x)

= - \frac{5}{2} cos^{4} (x)

解答补常数

= - \frac{5}{2} cos^{4} (x) + C

作图

流行的例子

derivative of sin(9)

\frac{d}{d x} (sin (9))

limit as x approaches 0 of e^{xsin(1/x)}

x \to 0 lim (e^{x s i n (\frac{1}{x})})

d er i v a t i v e y = 3

integral of 1/(sqrt(1-y^2))

\int \frac{1}{1 - y ^{2}} d y

derivative f(x)=x^{4x}

d er i v a t i v e f (x) = x^{4 x}