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Beliebt >

integral of 3x^4(2x-5)

Lösung

\int 3 x^{4} (2 x - 5) d x

Lösung

3 (\frac{2}{5} x^{6} - x^{5} - \frac{x ^{6}}{15}) + C

Schritte zur Lösung

\int 3 x^{4} (2 x - 5) d x

Entferne die Konstante:

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

= 3 \cdot \int x^{4} (2 x - 5) d x

Wende die partielle Integration an

: \frac{1}{5} x^{5} (2 x - 5) - \int \frac{2 x ^{5}}{5} d x

= 3 (\frac{1}{5} x^{5} (2 x - 5) - \int \frac{2 x ^{5}}{5} d x)

\int \frac{2 x ^{5}}{5} d x = \frac{x ^{6}}{15}

= 3 (\frac{1}{5} x^{5} (2 x - 5) - \frac{x ^{6}}{15})

Multipliziere aus

\frac{1}{5} x^{5} (2 x - 5) : \frac{2}{5} x^{6} - x^{5}

= 3 (\frac{2}{5} x^{6} - x^{5} - \frac{x ^{6}}{15})

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{2}{5} x^{6} - x^{5} - \frac{x ^{6}}{15}) + C

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integral of (x+9)/(x^2+5x)

\int \frac{x + 9}{x ^{2} + 5 x} d x

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\int \frac{x e ^{x} + 5}{x} d x

integral of (2x^4)/(x^5+1)

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

integral of 1/(sqrt(ax))

\int \frac{1}{a x} d x

integral of 4/((4x-3)ln(4x-3))

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