integral of (5sinh(x)+x^5)

Lösung

\int (5 sinh (x) + x^{5}) d x

5 cosh (x) + \frac{x ^{6}}{6} + C

Schritte zur Lösung

\int 5 sinh (x) + x^{5} 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 5 sinh (x) d x + \int x^{5} d x

\int 5 sinh (x) d x = 5 cosh (x)

\int x^{5} d x = \frac{x ^{6}}{6}

= 5 cosh (x) + \frac{x ^{6}}{6}

Füge eine Konstante zur Lösung hinzu

= 5 cosh (x) + \frac{x ^{6}}{6} + C

\int \frac{12 + 3 e ^{2 t}}{e ^{2 t}} d t

\int - 4 \frac{1 + x}{1 - x} d x

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

\int x cot^{2} (2) x^{2} d x

\int (8 x^{3} + 3 x^{2} + 5 x + 3) d x