integral of sh x/3

解答

\int s h \frac{x}{3} d x

\frac{h s x ^{2}}{6} + C

求解步骤

\int s h \frac{x}{3} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} h s \cdot \int x d x

化简

\frac{1}{3} h s : \frac{h s}{3}

= \frac{h s}{3} \cdot \int x d x

使用幂法则

= \frac{h s}{3} \cdot \frac{x ^{2}}{2}

化简

\frac{h s}{3} \cdot \frac{x ^{2}}{2} : \frac{h s x ^{2}}{6}

= \frac{h s x ^{2}}{6}

解答补常数

= \frac{h s x ^{2}}{6} + C

\int 29 arctan (x) d x

\frac{d}{d x} (e^{2 x - 3})

t an g e n t f (x) = x - 5 sin (x), at x = \frac{π}{2}

x \to - 7 + lim (\frac{x + 6}{x + 7})

\int \frac{x}{x ^{2} + 7} d x