integral from 3 to x of sec(t)tan(t)

解答

\int_{3}^{x} sec (t) tan (t) d t

sec (x) - sec (3)

求解步骤

\int_{3}^{x} sec (t) tan (t) d t

使用换元积分法

= \int_{s e c (3)}^{s e c (x)} 1 d u

常数积分:

\int a d x = a x

= [1 \cdot u]_{s e c (3)}^{s e c (x)}

化简

= [u]_{s e c (3)}^{s e c (x)}

带入上下限计算后得:

sec (x) - sec (3)

= sec (x) - sec (3)

\int_{0}^{1} 2 x (x^{2} + 3)^{4} d x

\int_{0}^{1} \frac{1}{4 x} + 9 d x

\int_{0}^{\infty} x \cdot e^{- 4 x} d x

\int_{0}^{2} \frac{1}{25} y d y

\int_{0}^{2} 3 x x^{2} + 4 a^{2} d x