integral of (3x-4/3 x^{3/2})

Lösung

\int (3 x - \frac{4}{3} x^{\frac{3}{2}}) d x

\frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int 3 x - \frac{4}{3} x^{\frac{3}{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 3 x d x - \int \frac{4}{3} x^{\frac{3}{2}} d x

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

\int \frac{4}{3} x^{\frac{3}{2}} d x = \frac{8}{15} x^{\frac{5}{2}}

= \frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}} + C

x \to 1 - lim (arcsin (\frac{1}{x}))

a re a y = ∣ x ∣, y = x^{2}

\int \frac{sin ( θ ) - 1}{cos ^{2} ( θ )} d θ

\frac{\partial}{\partial y} (e^{- x y})

\frac{\partial}{\partial x} (y e^{\frac{x}{y}} - z)