integral of 8xsec^2(x)

解答

\int 8 x sec^{2} (x) d x

8 (x tan (x) + ln ∣ cos (x) ∣) + C

求解步骤

\int 8 x sec^{2} (x) d x

提出常数:

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

= 8 \cdot \int x sec^{2} (x) d x

使用分布积分法

= 8 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 8 (x tan (x) - (- ln ∣ cos (x) ∣))

化简

= 8 (x tan (x) + ln ∣ cos (x) ∣)

解答补常数

= 8 (x tan (x) + ln ∣ cos (x) ∣) + C

\int x sin (2 a x) d x

d er i v a t i v e y = (1 + 6 x^{2}) (x - x^{2})

n = 1 \sum \infty \frac{5}{n ^{4}}

x \to \infty lim (\frac{x}{3 x})

\frac{d ^{2}}{d x ^{2}} (\frac{1}{4 x ^{2} + 5 x})