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

Lösung

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

x - 10 (\frac{1}{4} ln 4 x^{2} - 4 x + 8 + \frac{1}{2 7} arctan (\frac{2 x - 1}{7})) + 27 arctan (\frac{1}{7} (2 x - 1)) + C

Schritte zur Lösung

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

Lange Division

\frac{( x - 3 ) ^{2}}{x ^{2} - x + 2} : 1 + \frac{- 5 x + 7}{x ^{2} - x + 2}

= \int 1 + \frac{- 5 x + 7}{x ^{2} - x + 2} d x

Wende die Summenregel an:

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

= \int 1 d x + \int \frac{- 5 x + 7}{x ^{2} - x + 2} d x

\int 1 d x = x

\int \frac{- 5 x + 7}{x ^{2} - x + 2} d x = - 10 (\frac{1}{4} ln 4 x^{2} - 4 x + 8 + \frac{1}{2 7} arctan (\frac{2 x - 1}{7})) + 27 arctan (\frac{1}{7} (2 x - 1))

= x - 10 (\frac{1}{4} ln 4 x^{2} - 4 x + 8 + \frac{1}{2 7} arctan (\frac{2 x - 1}{7})) + 27 arctan (\frac{1}{7} (2 x - 1))

Füge eine Konstante zur Lösung hinzu

= x - 10 (\frac{1}{4} ln 4 x^{2} - 4 x + 8 + \frac{1}{2 7} arctan (\frac{2 x - 1}{7})) + 27 arctan (\frac{1}{7} (2 x - 1)) + C

d er i v a t i v e 2^{z} lo g_{2} (z)

y^{^{'}} + (\frac{3 y}{( 300 - t )}) = 4

\int \frac{64 x ^{2} - 1}{x} d x

\frac{\partial}{\partial x} (e^{x^{2} y} + x^{2} y)

\frac{d}{d x} (- \frac{y}{x ^{2}})