integral of csc(4x)cot(4x)+(13)/(x^2+16)

解答

\int csc (4 x) cot (4 x) + \frac{13}{x ^{2} + 16} d x

- \frac{1}{4} csc (4 x) + \frac{13}{4} arctan (\frac{x}{4}) + C

求解步骤

\int csc (4 x) cot (4 x) + \frac{13}{x ^{2} + 16} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int csc (4 x) cot (4 x) d x + \int \frac{13}{x ^{2} + 16} d x

\int csc (4 x) cot (4 x) d x = - \frac{1}{4} csc (4 x)

\int \frac{13}{x ^{2} + 16} d x = \frac{13}{4} arctan (\frac{x}{4})

= - \frac{1}{4} csc (4 x) + \frac{13}{4} arctan (\frac{x}{4})

解答补常数

= - \frac{1}{4} csc (4 x) + \frac{13}{4} arctan (\frac{x}{4}) + C

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