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受欢迎的微积分 >

积分 ((x^2+2x-3))/(x^4)

解答

积分

\frac{( x ^{2} + 2 x - 3 )}{x ^{4}}

解答

- \frac{1}{x} - \frac{1}{x ^{2}} + \frac{1}{x ^{3}} + C

求解步骤

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

乘开

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

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

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

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

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

= - \frac{1}{x} - \frac{1}{x ^{2}} - (- \frac{1}{x ^{3}})

化简

= - \frac{1}{x} - \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

解答补常数

= - \frac{1}{x} - \frac{1}{x ^{2}} + \frac{1}{x ^{3}} + C

作图

流行的例子

积分 y(1-y^2)^{1/2}

in t e g r a l y (1 - y^{2})^{\frac{1}{2}}

in t e g r a l 2 e^{- x}

积分 1/((1+x^2)^{0.5)}

in t e g r a l \frac{1}{( 1 + x ^{2} ) ^{0.5}}

积分 (-1)/(y+1)

in t e g r a l \frac{- 1}{y + 1}

in t e g r a l x^{2} e^{2} x