integral of (ex^2+pi)

解答

\int (e x^{2} + π) d x

\frac{e x ^{3}}{3} + π x + C

求解步骤

\int e x^{2} + π 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 e x^{2} d x + \int π d x

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

\int π d x = π x

= \frac{e x ^{3}}{3} + π x

解答补常数

= \frac{e x ^{3}}{3} + π x + C

x \to 0 lim (\frac{( 2 ∣ x ∣ )}{3 x})

\frac{\partial}{\partial x} (x^{2} + y^{2} - y cos (x))

\int - \frac{x ^{2}}{( - x + 1 ) ( x + 1 )} d x

x y^{^{'}} = ((1 - x) y + x^{2} + x^{3}), y (3) = 2

x \to 3 - lim (\frac{x}{∣ x ∣})