integral of x^7+7x+7/x+7

解答

\int x^{7} + 7 x + \frac{7}{x} + 7 d x

\frac{x ^{8}}{8} + \frac{7 x ^{2}}{2} + 7 ln ∣ x ∣ + 7 x + C

求解步骤

\int x^{7} + 7 x + \frac{7}{x} + 7 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

= \int x^{7} d x + \int 7 x d x + \int \frac{7}{x} d x + \int 7 d x

\int x^{7} d x = \frac{x ^{8}}{8}

\int 7 x d x = \frac{7 x ^{2}}{2}

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int 7 d x = 7 x

= \frac{x ^{8}}{8} + \frac{7 x ^{2}}{2} + 7 ln ∣ x ∣ + 7 x

解答补常数

= \frac{x ^{8}}{8} + \frac{7 x ^{2}}{2} + 7 ln ∣ x ∣ + 7 x + C