integral of 2x^2+1

解答

\int 2 x^{2} + 1 d x

\frac{2 x ^{3}}{3} + x + C

求解步骤

\int 2 x^{2} + 1 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 2 x^{2} d x + \int 1 d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int 1 d x = x

= \frac{2 x ^{3}}{3} + x

解答补常数

= \frac{2 x ^{3}}{3} + x + C

\int_{0}^{\frac{π}{2}} 30 cos^{5} (x) d x

t an g e n t f (x) = 3 x^{2} + 2 x, at x = 1

n = 1 \sum \infty (- 0.3)^{n}

x \to 0 lim (\frac{1}{3} x)

t an g e n t f (x) = 3 x - cos (x), at x = 0