integral of integral of tan(x)

Lösung

\int \int tan (x) d x d x

- i \frac{1}{2} Li_{2} (- e^{2 i x}) - \frac{i x ^{2}}{2} + x ln (1 + (- 1)^{\frac{2 x}{π}}) - x ln (cos (x)) + C x + C

Schritte zur Lösung

\int \int tan (x) d x d x

\int tan (x) d x = - ln (cos (x)) + C

= \int (- ln (cos (x)) + C) d x

\int (- ln (cos (x)) + C) d x = - i \frac{1}{2} Li_{2} (- e^{2 i x}) - \frac{i x ^{2}}{2} + x ln (1 + (- 1)^{\frac{2 x}{π}}) - x ln (cos (x)) + C x + C

= - i \frac{1}{2} Li_{2} (- e^{2 i x}) - \frac{i x ^{2}}{2} + x ln (1 + (- 1)^{\frac{2 x}{π}}) - x ln (cos (x)) + C x + C

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