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

f (x) = arcsin^{2} (x)

x \to 0 + lim (6 sin (x) ln (x))

\int \frac{x ^{8} + 1}{x ^{9} + 9 x} d x

l a pl a ce t r an s f or m 4^{t}

im pl i c i t \frac{d y}{d x}, y = \frac{6}{3 x ^{2} + 5}