integral of (pi-x)cos(n)x

解答

\int (π - x) cos (n) x d x

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

求解步骤

\int (π - x) cos (n) x d x

提出常数:

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

= cos (n) \cdot \int (π - x) x d x

乘开

(π - x) x : π x - x^{2}

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

\int π x d x = \frac{π x ^{2}}{2}

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

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

解答补常数

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

\int (\frac{4 x ^{2} + 7 x}{x ^{2}}) d x

\int a e^{7 x} d x

\int sin (6 e^{x}) d x

\int \frac{1}{u + 2} d u

\int e^{\frac{2}{y}} d y