integral of ln((3x)^2)

Lösung

\int ln ((3 x)^{2}) d x

2 x ln (3 x) - 2 x + C

Schritte zur Lösung

\int ln ((3 x)^{2}) d x

Wende die partielle Integration an

= x ln (9 x^{2}) - \int 2 d x

\int 2 d x = 2 x

= x ln (9 x^{2}) - 2 x

Vereinfache

ln (9 x^{2}) : 2 ln (3 x)

= 2 x ln (3 x) - 2 x

Füge eine Konstante zur Lösung hinzu

= 2 x ln (3 x) - 2 x + C

\int \frac{- 8 x ^{2} + 16 x + 8}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

\int_{1}^{7} x - 1 d x

\int \frac{ln ( ln ( 3 x ) )}{3 x} d x

x \to 3 lim (5 x^{3} - 3 x + x - 6)

\frac{\partial}{\partial x} (am x^{b} m y^{1 - b})