integral of sin(1/7)x

解答

\int sin (\frac{1}{7}) x d x

\frac{1}{2} sin (\frac{1}{7}) x^{2} + C

求解步骤

\int sin (\frac{1}{7}) x d x

提出常数:

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

= sin (\frac{1}{7}) \cdot \int x d x

使用幂法则

= sin (\frac{1}{7}) \frac{x ^{2}}{2}

化简

sin (\frac{1}{7}) \frac{x ^{2}}{2} : \frac{1}{2} sin (\frac{1}{7}) x^{2}

= \frac{1}{2} sin (\frac{1}{7}) x^{2}

解答补常数

= \frac{1}{2} sin (\frac{1}{7}) x^{2} + C

h \to 0 lim \frac{( ( h - 5 ) ^{2} - 25 )}{( h )}

\frac{d}{d y} (2 x y^{3})

\int - \frac{1}{s} e^{- s t} d t

\int x (4 x + 5)^{8} d x

x \to \infty lim (5^{- \frac{1}{x}})