integral of (sec(x))/(sec(x)-cos(x))

解答

\int \frac{sec ( x )}{sec ( x ) - cos ( x )} d x

- cot (x) + C

求解步骤

\int \frac{sec ( x )}{sec ( x ) - cos ( x )} d x

使用三角恒等式改写

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

使用三角恒等式改写

= \int csc^{2} (x) d x

使用积分常见定则:

\int csc^{2} (x) d x = - cot (x)

= - cot (x)

解答补常数

= - cot (x) + C

\frac{d}{d x} (- 18)

\int \frac{x}{2 x} d x

\frac{d}{d x} (x^{4} + 3 x^{3} - x^{2})

in v erse l a pl a ce \frac{s + 1}{( s ^{2} - 4 s ) ( s + 5 )}

x \to 2 lim (ln (x^{2} - 4))