integral of tan(X)

解答

\int tan (X) d X

- ln ∣ cos (X) ∣ + C

求解步骤

\int tan (X) d X

使用三角恒等式改写

= \int \frac{sin ( X )}{cos ( X )} d X

使用换元积分法

= \int - \frac{1}{u} d u

提出常数:

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

= - \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

u = cos (X)

代回

= - ln ∣ cos (X) ∣

解答补常数

= - ln ∣ cos (X) ∣ + C

d er i v a t i v e y = \frac{6}{x}

\frac{d}{d x} (4 x x)

\int \frac{6}{6 x + 1} d x

\frac{d}{d x} (\frac{4 x ^{2} + 6 x + 8}{x})

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