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Beliebt Rechnen >

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

Lösung

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

Lösung

2 x ln (x + 1) - 2 (x + 1 - ln ∣ x + 1 ∣) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{2 x}{x + 1} d x = 2 (x + 1 - ln ∣ x + 1 ∣)

= x ln ((x + 1)^{2}) - 2 (x + 1 - ln ∣ x + 1 ∣)

Wende log Regel an

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

angenommen

x \geq 0

= 2 x ln (x + 1) - 2 (x + 1 - ln ∣ x + 1 ∣)

Füge eine Konstante zur Lösung hinzu

= 2 x ln (x + 1) - 2 (x + 1 - ln ∣ x + 1 ∣) + C

Graph

Beliebte Beispiele

integral of 3^x+x^3+3/x

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

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

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

integral of x^2(1-x^3)^3

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

integral of sin(x/2)cos(nx)

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

integral of ln(x/(1-x))

\int ln (\frac{x}{1 - x}) d x