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

Lösung

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

x ln (ln (x)) + C

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int ln (ln (x)) d x = x ln (ln (x)) - Ei (ln (x))

\int \frac{1}{ln ( x )} d x = Ei (ln (x))

= x ln (ln (x)) - Ei (ln (x)) + Ei (ln (x))

Vereinfache

= x ln (ln (x))

Füge eine Konstante zur Lösung hinzu

= x ln (ln (x)) + C

\int - 6 t^{\frac{1}{2}} + 7 d t

\int (x^{3} + 1)^{4} 3 x^{2} d x

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

\int (- \frac{2}{x} + 3 cos (6 x)) d x

\int 1 + (x^{3} - \frac{1}{4 x ^{3}})^{2} d x