integral of ln(4-2x)

Lösung

\int ln (4 - 2 x) d x

x ln (4 - 2 x) - 2 ln ∣ 2 - x ∣ - x + C

Schritte zur Lösung

\int ln (4 - 2 x) d x

Wende die partielle Integration an

= x ln (4 - 2 x) - \int - \frac{x}{2 - x} d x

\int - \frac{x}{2 - x} d x = 2 ln ∣ 2 - x ∣ + x

= x ln (4 - 2 x) - (2 ln ∣ 2 - x ∣ + x)

Vereinfache

= x ln (4 - 2 x) - 2 ln ∣ 2 - x ∣ - x

Füge eine Konstante zur Lösung hinzu

= x ln (4 - 2 x) - 2 ln ∣ 2 - x ∣ - x + C

\int 10 cos (x) + sec^{2} (x) d x

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

\int \frac{cos ( 2 x )}{2 + 3 sin ( 2 x )} d x

\int x 2 x^{2} - 3 d x

\int \frac{2 x ^{2}}{x ^{3} x ^{6} - 9} d x