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受欢迎的微积分 >

integral of etan(x)

解答

\int e tan (x) d x

解答

- e ln ∣ cos (x) ∣ + C

求解步骤

\int e tan (x) d x

提出常数:

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

= e \cdot \int tan (x) d x

使用三角恒等式改写

= e \cdot \int \frac{sin ( x )}{cos ( x )} d x

使用换元积分法

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

提出常数:

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

= e (- \int \frac{1}{u} d u)

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= e (- ln ∣ u ∣)

u = cos (x)

代回

= e (- ln ∣ cos (x) ∣)

化简

= - e ln ∣ cos (x) ∣

解答补常数

= - e ln ∣ cos (x) ∣ + C

作图

流行的例子

(d^2)/(dx^2)(cos^2(t))

\frac{d ^{2}}{d x ^{2}} (cos^{2} (t))

integral of (sin(2x))/(cos^2(2x)+5)

\int \frac{sin ( 2 x )}{cos ^{2} ( 2 x ) + 5} d x

limit as x approaches 1 of 4x

x \to 1 lim (4 x)

integral of sec^2(t)

\int sec^{2} (t) d t

limit as x approaches 0+of ((e^x))/(2^x)

x \to 0 + lim (\frac{( e ^{x} )}{2 ^{x}})