integral of 9x^2ln(x)

Lösung

\int 9 x^{2} ln (x) d x

3 x^{3} ln (x) - x^{3} + C

Schritte zur Lösung

\int 9 x^{2} ln (x) d x

Entferne die Konstante:

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

= 9 \cdot \int x^{2} ln (x) d x

Wende die partielle Integration an

= 9 (\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x)

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= 9 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Vereinfache

9 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) : 3 x^{3} ln (x) - x^{3}

= 3 x^{3} ln (x) - x^{3}

Füge eine Konstante zur Lösung hinzu

= 3 x^{3} ln (x) - x^{3} + C

\frac{d}{d x} ((1 - \frac{x}{2})^{e^{x^{2}}})

x \frac{d y}{d x} + (3 x + 1) y = e^{3 x}

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\int_{2}^{\frac{1}{x}} arctan (t) d t

\int_{- 5}^{0} (4 + 25 - x^{2}) d x