integral of 3-1/(x^4)+1/(x^2)

解答

\int 3 - \frac{1}{x ^{4}} + \frac{1}{x ^{2}} d x

3 x + \frac{1}{3 x ^{3}} - \frac{1}{x} + C

求解步骤

\int 3 - \frac{1}{x ^{4}} + \frac{1}{x ^{2}} 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 3 d x - \int \frac{1}{x ^{4}} d x + \int \frac{1}{x ^{2}} d x

\int 3 d x = 3 x

\int \frac{1}{x ^{4}} d x = - \frac{1}{3 x ^{3}}

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= 3 x - (- \frac{1}{3 x ^{3}}) - \frac{1}{x}

化简

= 3 x + \frac{1}{3 x ^{3}} - \frac{1}{x}

解答补常数

= 3 x + \frac{1}{3 x ^{3}} - \frac{1}{x} + C

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