integral of x*ln^5(x)

Lösung

\int x \cdot ln^{5} (x) d x

\frac{1}{2} x^{2} ln^{5} (x) - \frac{5}{8} (2 x^{2} ln^{4} (x) - 4 x^{2} ln^{3} (x) + 6 x^{2} ln^{2} (x) - 6 x^{2} ln (x) + 3 x^{2}) + C

Schritte zur Lösung

\int x ln^{5} (x) d x

Wende die partielle Integration an

= \frac{1}{2} x^{2} ln^{5} (x) - \int \frac{5}{2} x ln^{4} (x) d x

\int \frac{5}{2} x ln^{4} (x) d x = \frac{5}{8} (2 x^{2} ln^{4} (x) - 4 x^{2} ln^{3} (x) + 6 x^{2} ln^{2} (x) - 6 x^{2} ln (x) + 3 x^{2})

= \frac{1}{2} x^{2} ln^{5} (x) - \frac{5}{8} (2 x^{2} ln^{4} (x) - 4 x^{2} ln^{3} (x) + 6 x^{2} ln^{2} (x) - 6 x^{2} ln (x) + 3 x^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} ln^{5} (x) - \frac{5}{8} (2 x^{2} ln^{4} (x) - 4 x^{2} ln^{3} (x) + 6 x^{2} ln^{2} (x) - 6 x^{2} ln (x) + 3 x^{2}) + C

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{x} + x e^{2 x}

f (x) = cot (x^{2})

\int_{- 1}^{0} x^{3} - x^{2} - 2 x d x

\int x^{4} cos (2 x) d x

a re a 9 - x^{2}, y = 0