integral of x^2-4x+7

Lösung

\int x^{2} - 4 x + 7 d x

\frac{x ^{3}}{3} - 2 x^{2} + 7 x + C

Schritte zur Lösung

\int x^{2} - 4 x + 7 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 x^{2} d x - \int 4 x d x + \int 7 d x

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

\int 4 x d x = 2 x^{2}

\int 7 d x = 7 x

= \frac{x ^{3}}{3} - 2 x^{2} + 7 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - 2 x^{2} + 7 x + C

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

\frac{\partial}{\partial x} (sin (x^{2} y - 4 x y^{2}))

\int \frac{7}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

d er i v a t i v e \frac{4}{3 x ^{2}}

t an g e n t f (x) = x^{2} - \frac{1}{x}, (- 1, 0)