integral of 10xsec^2(x)

解答

\int 10 x sec^{2} (x) d x

10 (x tan (x) + ln ∣ cos (x) ∣) + C

求解步骤

\int 10 x sec^{2} (x) d x

提出常数:

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

= 10 \cdot \int x sec^{2} (x) d x

使用分布积分法

= 10 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 10 (x tan (x) - (- ln ∣ cos (x) ∣))

化简

= 10 (x tan (x) + ln ∣ cos (x) ∣)

解答补常数

= 10 (x tan (x) + ln ∣ cos (x) ∣) + C

x \to - 6 lim (\frac{x ^{2} - 1}{6 - x})

\frac{d}{d x} (\frac{e ^{3 x^{2}}}{5 x})

d er i v a t i v e f (x) = 16 4 x

\int \frac{sin ^{7} ( 10 x )}{cos ^{4} ( 10 x )} d x

\frac{\partial}{\partial y} (f (x, y) (x + y))