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

解答

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

18 x - \frac{8}{x} + C

求解步骤

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

乘开

(3 x - 2)^{2} + (3 x + 2)^{2} : 18 x^{2} + 8

= \int \frac{18 x ^{2} + 8}{x ^{2}} d x

乘开

\frac{18 x ^{2} + 8}{x ^{2}} : 18 + \frac{8}{x ^{2}}

= \int 18 + \frac{8}{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 18 d x + \int \frac{8}{x ^{2}} d x

\int 18 d x = 18 x

\int \frac{8}{x ^{2}} d x = - \frac{8}{x}

= 18 x - \frac{8}{x}

解答补常数

= 18 x - \frac{8}{x} + C

d er i v a t i v e \frac{cos ( 2 x )}{sin ( 2 x )}

\int (4 x^{5} + 3 x + 8) d x

f^{^{'}} (x) = 8 x^{3} - 6 x^{2} + 10 x - 9, f (1) = 24

ma c l a u r in 1 - x^{2}

d er i v a t i v e y = \frac{x}{7 + x}