integral of (cos(3pi)x)/2

解答

\int \frac{cos ( 3 π ) x}{2} d x

- \frac{x ^{2}}{4} + C

求解步骤

\int \frac{cos ( 3 π ) x}{2} d x

提出常数:

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

= \frac{cos ( 3 π )}{2} \cdot \int x d x

\frac{cos ( 3 π )}{2} = - \frac{1}{2}

= (- \frac{1}{2}) \cdot \int x d x

使用幂法则

= (- \frac{1}{2}) \frac{x ^{2}}{2}

化简

(- \frac{1}{2}) \frac{x ^{2}}{2} : - \frac{x ^{2}}{4}

= - \frac{x ^{2}}{4}

解答补常数

= - \frac{x ^{2}}{4} + C

3 y^{^{''}} - 4 y^{^{'}} - 15 y = 0, y (0) = - 7, y^{^{'}} (0) = - 2

\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{x})

\int \frac{1}{sin ^{2} ( x ) cos ^{2} ( x )} d x

d er i v a t i v e \frac{8}{( 1 - x ) ^{2}}

y^{^{''}} + y = 6 e^{- t}, y^{^{'}} (0) = 0, y (0) = 0