integral of (3^4+x^{15})

解答

\int (3^{4} + x^{15}) d x

81 x + \frac{x ^{16}}{16} + C

求解步骤

\int 3^{4} + x^{15} 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 3^{4} d x + \int x^{15} d x

\int 3^{4} d x = 81 x

\int x^{15} d x = \frac{x ^{16}}{16}

= 81 x + \frac{x ^{16}}{16}

解答补常数

= 81 x + \frac{x ^{16}}{16} + C

\int x^{2} a^{2} - x^{2} d x

f (x) = x^{3} - x

t an g e n t y = (2 x - 1) (x + 4), (1, 5)

d er i v a t i v e \frac{12}{x ^{5}} - \frac{7}{5 x}

\frac{d}{d x} ((x^{3} - 2 x)^{x^{2} - 3})