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Beliebt Rechnen >

integral of ln(1-4x)

Lösung

\int ln (1 - 4 x) d x

Lösung

- \frac{1}{4} ln (1 - 4 x) + x ln (1 - 4 x) + \frac{1}{4} - x + C

Schritte zur Lösung

\int ln (1 - 4 x) d x

Wende U-Substitution an

= \int - \frac{1}{4} ln (u) d u

Entferne die Konstante:

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

= - \frac{1}{4} \cdot \int ln (u) d u

Wende die partielle Integration an

= - \frac{1}{4} (u ln (u) - \int 1 d u)

\int 1 d u = u

= - \frac{1}{4} (u ln (u) - u)

Setze in

u = 1 - 4 x

ein

= - \frac{1}{4} ((1 - 4 x) ln (1 - 4 x) - (1 - 4 x))

Vereinfache

- \frac{1}{4} ((1 - 4 x) ln (1 - 4 x) - (1 - 4 x)) : - \frac{1}{4} ln (1 - 4 x) + x ln (1 - 4 x) + \frac{1}{4} - x

= - \frac{1}{4} ln (1 - 4 x) + x ln (1 - 4 x) + \frac{1}{4} - x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} ln (1 - 4 x) + x ln (1 - 4 x) + \frac{1}{4} - x + C

Graph

Beliebte Beispiele

integral of (x^2+4x+1)/((x^2-1)(x+3))

\int \frac{x ^{2} + 4 x + 1}{( x ^{2} - 1 ) ( x + 3 )} d x

integral of (x^2)/((x^2+1)^3)

\int \frac{x ^{2}}{( x ^{2} + 1 ) ^{3}} d x

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

\int (\frac{1}{1 + x ^{4}}) d x

integral of-3ln(x)

\int - 3 ln (x) d x

integral of 1/((e^{2x)-1)^{1/2}}

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