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Beliebt Rechnen >

integral of ln(x^{x^2})

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

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

Wende die partielle Integration an

= \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}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of sin(2x)ln(cos(x))

\int sin (2 x) ln (cos (x)) d x

integral of (8x)/(4x^2-9)

\int \frac{8 x}{4 x ^{2} - 9} d x

integral of-sec^2((9x)/8)

\int - sec^{2} (\frac{9 x}{8}) d x

integral of (9^x)/(1+81^x)

\int \frac{9 ^{x}}{1 + 8 1 ^{x}} d x

integral of y^3ln^3(y)

\int y^{3} ln^{3} (y) d y