integral of x\sqrt[9]{4+x^2}

Lösung

\int x 9 4 + x^{2} d x

\frac{9}{20} (4 + x^{2})^{\frac{10}{9}} + C

Schritte zur Lösung

\int x 9 4 + x^{2} d x

Wende U-Substitution an

= \int \frac{9 u}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int 9 u d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{9}{10} u^{\frac{10}{9}}

Setze in

u = 4 + x^{2}

ein

= \frac{1}{2} \cdot \frac{9}{10} (4 + x^{2})^{\frac{10}{9}}

Vereinfache

\frac{1}{2} \cdot \frac{9}{10} (4 + x^{2})^{\frac{10}{9}} : \frac{9}{20} (4 + x^{2})^{\frac{10}{9}}

= \frac{9}{20} (4 + x^{2})^{\frac{10}{9}}

Füge eine Konstante zur Lösung hinzu

= \frac{9}{20} (4 + x^{2})^{\frac{10}{9}} + C

in v erse l a pl a ce \frac{e ^{- s}}{s ^{5}}

x \to 0 lim (\frac{( 4 ^{x} - 1 )}{x})

\int sin (7 x - 10) d x

x \to \infty lim (4 x^{3})

\frac{\partial}{\partial y} (ln (\frac{x ^{2}}{y}))