integral of ((6+x^2)/x)

解答

\int (\frac{6 + x ^{2}}{x}) d x

6 ln ∣ x ∣ + \frac{x ^{2}}{2} + C

求解步骤

\int \frac{6 + x ^{2}}{x} d x

乘开

\frac{6 + x ^{2}}{x} : \frac{6}{x} + x

= \int \frac{6}{x} + x 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{6}{x} d x + \int x d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

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

= 6 ln ∣ x ∣ + \frac{x ^{2}}{2}

解答补常数

= 6 ln ∣ x ∣ + \frac{x ^{2}}{2} + C

\int tan (x) + sec^{2} (x) d x

\int \frac{( 6 x - 6 )}{x ^{2} - 2 x + 5} d x

\int (10 x + 2) d x

\int cos (\frac{2 x}{5}) d x

\int \frac{1}{51 - 70 x - 25 x ^{2}} d x