integral of (2x^3+x)(x^4+x^2)^{108}

Lösung

\int (2 x^{3} + x) (x^{4} + x^{2})^{108} d x

\frac{1}{218} (x^{4} + x^{2})^{109} + C

Schritte zur Lösung

\int (2 x^{3} + x) (x^{4} + x^{2})^{108} d x

Wende U-Substitution an

= \int \frac{u ^{108}}{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 u^{108} d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{u ^{109}}{109}

Setze in

u = x^{4} + x^{2}

ein

= \frac{1}{2} \cdot \frac{( x ^{4} + x ^{2} ) ^{109}}{109}

Vereinfache

\frac{1}{2} \cdot \frac{( x ^{4} + x ^{2} ) ^{109}}{109} : \frac{1}{218} (x^{4} + x^{2})^{109}

= \frac{1}{218} (x^{4} + x^{2})^{109}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{218} (x^{4} + x^{2})^{109} + C

f (x) = sin (9 x)

\frac{d}{d x} (500 x - 2 x^{2})

x \frac{d y}{d x} = 2 x e^{x} - y + 6 x^{2}

\frac{d}{d x} (\frac{24}{x ^{2} + 4 x})

l a pl a ce t r an s f or m sin (2 t) sin (t)