integral of 6xsec^2(x)

解答

\int 6 x sec^{2} (x) d x

6 (x tan (x) + ln ∣ cos (x) ∣) + C

求解步骤

\int 6 x sec^{2} (x) d x

提出常数:

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

= 6 \cdot \int x sec^{2} (x) d x

使用分布积分法

= 6 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 6 (x tan (x) - (- ln ∣ cos (x) ∣))

化简

= 6 (x tan (x) + ln ∣ cos (x) ∣)

解答补常数

= 6 (x tan (x) + ln ∣ cos (x) ∣) + C

x y + 2 x \frac{d y}{d x} = y

x \to 0 + lim (\frac{1}{x} - ln (x))

n = 0 \sum \infty (\frac{x + 9}{2})^{n}

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

x \to + 1 lim (x (x - 2))