integral of r^3+2r

解答

\int r^{3} + 2 r d r

\frac{r ^{4}}{4} + r^{2} + C

求解步骤

\int r^{3} + 2 r d r

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 r^{3} d r + \int 2 r d r

\int r^{3} d r = \frac{r ^{4}}{4}

\int 2 r d r = r^{2}

= \frac{r ^{4}}{4} + r^{2}

解答补常数

= \frac{r ^{4}}{4} + r^{2} + C

\frac{d}{d t} (2 cos^{2} (t))

\int x (3 x^{2} - 5)^{10} d x

\int x^{4} e^{5 x} d x

f (x) = \frac{3}{x + 5}

d er i v a t i v e y = \frac{3}{x ^{6}} + \frac{1}{x ^{5}} - \frac{7}{x ^{2}}