integral of 3x^2-5x+7/x+2e^3

Lösung

\int 3 x^{2} - 5 x + \frac{7}{x} + 2 e^{3} d x

x^{3} - \frac{5 x ^{2}}{2} + 7 ln ∣ x ∣ + 2 e^{3} x + C

Schritte zur Lösung

\int 3 x^{2} - 5 x + \frac{7}{x} + 2 e^{3} 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 3 x^{2} d x - \int 5 x d x + \int \frac{7}{x} d x + \int 2 e^{3} d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int \frac{7}{x} d x = 7 ln ∣ x ∣

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

= x^{3} - \frac{5 x ^{2}}{2} + 7 ln ∣ x ∣ + 2 e^{3} x

Füge eine Konstante zur Lösung hinzu

= x^{3} - \frac{5 x ^{2}}{2} + 7 ln ∣ x ∣ + 2 e^{3} x + C

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

\int \frac{8}{4 + x ^{2}} d x

d er i v a t i v e y = - 2 x sin (x^{2})

in v erse l a pl a ce \frac{s - 3}{s ^{2} - 3 s + 2}

x \to 10 lim (\frac{10 x}{2 x + 5})