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Beliebt Rechnen >

integral of-ln|cos(x)|

Lösung

\int - ln ∣ cos (x) ∣ d x

Lösung

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

Schritte zur Lösung

\int - ln ∣ cos (x) ∣ d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int ln ∣ cos (x) ∣ d x

Wende die partielle Integration an

= - (x ln ∣ cos (x) ∣ - \int - x tan (x) d x)

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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integral of cos(20x)cos(13x)

\int cos (20 x) cos (13 x) d x

derivative y=-1.97x^2+0.51x+8.1

d er i v a t i v e y = - 1.97 x^{2} + 0.51 x + 8.1

integral of sin(26x)cos(17x)

\int sin (26 x) cos (17 x) d x

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\int x sin (k x) d x