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受欢迎的微积分 >

integral of 3cos^2(x)sin(x)

解答

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

解答

- cos^{3} (x) + C

求解步骤

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

提出常数:

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

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

使用换元积分法

= 3 \cdot \int - u^{2} d u

提出常数:

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

= 3 (- \int u^{2} d u)

使用幂法则

= 3 (- \frac{u ^{3}}{3})

u = cos (x)

代回

= 3 (- \frac{cos ^{3} ( x )}{3})

化简

3 (- \frac{cos ^{3} ( x )}{3}) : - cos^{3} (x)

= - cos^{3} (x)

解答补常数

= - cos^{3} (x) + C

作图

流行的例子

integral of (2t^2+3)^{4/3}t^3

\int (2 t^{2} + 3)^{\frac{4}{3}} t^{3} d t

derivative f(x)=(x^2+3x-1)e^x

d er i v a t i v e f (x) = (x^{2} + 3 x - 1) e^{x}

limit as n approaches infinity of |((2n)^{2n})/((2n+2)^{2n)}|

n \to \infty lim (\frac{( 2 n ) ^{2 n}}{( 2 n + 2 ) ^{2 n}})

limit as x approaches 2 of 3x-1

x \to 2 lim (3 x - 1)

sum from n=1 to infinity of 5^nx^n

n = 1 \sum \infty 5^{n} x^{n}