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Beliebt Rechnen >

integral of (4x-1)*ln(x)

Lösung

\int (4 x - 1) \cdot ln (x) d x

Lösung

2 x^{2} ln (x) - x ln (x) - x^{2} + x + C

Schritte zur Lösung

\int (4 x - 1) ln (x) d x

Wende die partielle Integration an

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

\int 2 x - 1 d x = x^{2} - x

= ln (x) (2 x^{2} - x) - (x^{2} - x)

Vereinfache

ln (x) (2 x^{2} - x) - (x^{2} - x) : 2 x^{2} ln (x) - x ln (x) - x^{2} + x

= 2 x^{2} ln (x) - x ln (x) - x^{2} + x

Füge eine Konstante zur Lösung hinzu

= 2 x^{2} ln (x) - x ln (x) - x^{2} + x + C

Graph

Beliebte Beispiele

integral of 2e^x+sec(x)tan(x)-sqrt(x)

\int 2 e^{x} + sec (x) tan (x) - x d x

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\int a x + b y d x

integral of (2)5^{x^2+7}

\int (2) 5^{x^{2} + 7} d x

integral of (x^3)/(3x^2+3)

\int \frac{x ^{3}}{3 x ^{2} + 3} d x

integral of (2x+1)*(x^2+x+1)

\int (2 x + 1) \cdot (x^{2} + x + 1) d x