integral of (8x^7-7/(x^7))

解答

\int (8 x^{7} - \frac{7}{x ^{7}}) d x

x^{8} + \frac{7}{6 x ^{6}} + C

求解步骤

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

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

\int \frac{7}{x ^{7}} d x = - \frac{7}{6 x ^{6}}

= x^{8} - (- \frac{7}{6 x ^{6}})

化简

= x^{8} + \frac{7}{6 x ^{6}}

解答补常数

= x^{8} + \frac{7}{6 x ^{6}} + C

d er i v a t i v e y = x^{10}

d er i v a t i v e f (x) = - \frac{16}{x ^{3}}

\frac{d}{d x} (a x^{2} (x - 3) + b x^{4} (ln (\frac{x}{3})))

\int \frac{2 t}{1 - t ^{2}} d t

n = 1 \sum \infty n \cdot 2^{- n}