integral of x^2(3x^2+9)^2

解答

\int x^{2} (3 x^{2} + 9)^{2} d x

\frac{9 x ^{7}}{7} + \frac{54 x ^{5}}{5} + 27 x^{3} + C

求解步骤

\int x^{2} (3 x^{2} + 9)^{2} d x

乘开

x^{2} (3 x^{2} + 9)^{2} : 9 x^{6} + 54 x^{4} + 81 x^{2}

= \int 9 x^{6} + 54 x^{4} + 81 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

= \int 9 x^{6} d x + \int 54 x^{4} d x + \int 81 x^{2} d x

\int 9 x^{6} d x = \frac{9 x ^{7}}{7}

\int 54 x^{4} d x = \frac{54 x ^{5}}{5}

\int 81 x^{2} d x = 27 x^{3}

= \frac{9 x ^{7}}{7} + \frac{54 x ^{5}}{5} + 27 x^{3}

解答补常数

= \frac{9 x ^{7}}{7} + \frac{54 x ^{5}}{5} + 27 x^{3} + C

\int csc^{3} (x) cot^{3} (x) d x

x \to \infty lim (\frac{1}{1 0 ^{2^{x}}})

\frac{d}{d j} (- 4 i + 5 j)

t a y l or cos (x), x = 0

t \to 0 lim (\frac{1}{t})