integral of (x+4)cos(n)pix

解答

\int (x + 4) cos (n) π x d x

cos (n) π (\frac{x ^{3}}{3} + 2 x^{2}) + C

求解步骤

\int (x + 4) cos (n) π x d x

提出常数:

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

= cos (n) π \cdot \int (x + 4) x d x

乘开

(x + 4) x : x^{2} + 4 x

= cos (n) π \cdot \int x^{2} + 4 x d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= cos (n) π (\int x^{2} d x + \int 4 x d x)

\int x^{2} d x = \frac{x ^{3}}{3}

\int 4 x d x = 2 x^{2}

= cos (n) π (\frac{x ^{3}}{3} + 2 x^{2})

解答补常数

= cos (n) π (\frac{x ^{3}}{3} + 2 x^{2}) + C

\int 14 sin^{2} (x) cos^{3} (x) d x

\frac{\partial}{\partial x} (\frac{1}{\frac{1}{x} + \frac{c}{x} + k})

\frac{\partial}{\partial x} (- y (y + sin (x)))

s im pl i f y 1 - \frac{3 x}{x ^{3} + 27}

\int \frac{1}{x ^{2} + 12 x + 35} d x