integral from 0 to pi/6 of 1/(cos^2(8x))

解答

\int_{0}^{\frac{π}{6}} \frac{1}{cos ^{2} ( 8 x )} d x

发散

求解步骤

\int_{0}^{\frac{π}{6}} \frac{1}{cos ^{2} ( 8 x )} d x

取

\frac{1}{cos ^{2} ( 8 x )}

的分母，令其等于零:

x = \frac{π}{16}

如果存在

b, a < b < c, f (b) =

无定义

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{\frac{π}{16}} \frac{1}{cos ^{2} ( 8 x )} d x + \int_{\frac{π}{16}}^{\frac{π}{6}} \frac{1}{cos ^{2} ( 8 x )} d x

\int_{0}^{\frac{π}{16}} \frac{1}{cos ^{2} ( 8 x )} d x =

发散

如果表达式有部分发散，则整个表达式发散

= 发散

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