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Beliebt >

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

Lösung

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

Lösung

- \frac{ln ( 1 + 3 x )}{x} + 3 (ln ∣ x ∣ - ln ∣ 3 x + 1 ∣) + C

Schritte zur Lösung

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

Wende die partielle Integration an

: - \frac{ln ( 1 + 3 x )}{x} - \int - \frac{3}{x ( 1 + 3 x )} d x

= - \frac{ln ( 1 + 3 x )}{x} - \int - \frac{3}{x ( 1 + 3 x )} d x

\int - \frac{3}{x ( 1 + 3 x )} d x = - 3 (ln ∣ x ∣ - ln ∣ 3 x + 1 ∣)

= - \frac{ln ( 1 + 3 x )}{x} - (- 3 (ln ∣ x ∣ - ln ∣ 3 x + 1 ∣))

Vereinfache

= - \frac{ln ( 1 + 3 x )}{x} + 3 (ln ∣ x ∣ - ln ∣ 3 x + 1 ∣)

Füge eine Konstante zur Lösung hinzu

= - \frac{ln ( 1 + 3 x )}{x} + 3 (ln ∣ x ∣ - ln ∣ 3 x + 1 ∣) + C

Beliebte Beispiele

integral of (ln(x))/(x^{3/2)}

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

integral of 1/(x(ln(x))^{17)}

\int \frac{1}{x ( ln ( x ) ) ^{17}} d x

integral of 1/(x5+1)

\int \frac{1}{x 5 + 1} d x

integral of 1/(sqrt(1-\frac{x^2){81)}}

\int \frac{1}{1 - \frac{x ^{2}}{81}} d x

integral of 5/((2x+1)(x-2))

\int \frac{5}{( 2 x + 1 ) ( x - 2 )} d x