integral of x^4sqrt(9+x^5)

Lösung

\int x^{4} 9 + x^{5} d x

\frac{2}{15} (9 + x^{5})^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{4} 9 + x^{5} d x

Wende U-Substitution an

= \int \frac{u}{5} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int u d u

Wende die Potenzregel an

= \frac{1}{5} \cdot \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = 9 + x^{5}

ein

= \frac{1}{5} \cdot \frac{2}{3} (9 + x^{5})^{\frac{3}{2}}

Vereinfache

\frac{1}{5} \cdot \frac{2}{3} (9 + x^{5})^{\frac{3}{2}} : \frac{2}{15} (9 + x^{5})^{\frac{3}{2}}

= \frac{2}{15} (9 + x^{5})^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{15} (9 + x^{5})^{\frac{3}{2}} + C

\int 11 x^{\frac{4}{7}} + 4 x^{- \frac{6}{7}} d x

\frac{d}{d x} (\frac{x ^{2}}{7})

t an g e n t f (x) = 2 x^{3} - 4 x^{2}, at x = 1

\int_{1}^{5} \frac{5}{x ^{2} + 4 x + 4} d x

\frac{\partial}{\partial y} (\frac{x ^{2}}{1 + y ^{3}})