integral of ln(3-x)

Lösung

\int ln (3 - x) d x

- 3 ln (3 - x) + x ln (3 - x) + 3 - x + C

Schritte zur Lösung

\int ln (3 - x) d x

Wende U-Substitution an

= \int - ln (u) d u

Entferne die Konstante:

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

= - \int ln (u) d u

Wende die partielle Integration an

= - (u ln (u) - \int 1 d u)

\int 1 d u = u

= - (u ln (u) - u)

Setze in

u = 3 - x

ein

= - ((3 - x) ln (3 - x) - (3 - x))

Vereinfache

- ((3 - x) ln (3 - x) - (3 - x)) : - 3 ln (3 - x) + x ln (3 - x) + 3 - x

= - 3 ln (3 - x) + x ln (3 - x) + 3 - x

Füge eine Konstante zur Lösung hinzu

= - 3 ln (3 - x) + x ln (3 - x) + 3 - x + C

\int_{1}^{2} \frac{x - 1}{2 x} d x

\frac{\partial}{\partial y} (sin (\frac{5 x}{y}))

a re a y = \frac{4}{x}, y = x, y = 4

\int 5 x^{2} (x^{3} + 1)^{10} d x

d er i v a t i v e f (x) = (5 x^{3} + 4) (3 x^{7} - 5)