integral of (\sqrt[10]{x}+\sqrt[11]{x})

Lösung

\int (10 x + 11 x) d x

\frac{10}{11} x^{\frac{11}{10}} + \frac{11}{12} x^{\frac{12}{11}} + C

Schritte zur Lösung

\int 10 x + 11 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 10 x d x + \int 11 x d x

\int 10 x d x = \frac{10}{11} x^{\frac{11}{10}}

\int 11 x d x = \frac{11}{12} x^{\frac{12}{11}}

= \frac{10}{11} x^{\frac{11}{10}} + \frac{11}{12} x^{\frac{12}{11}}

Füge eine Konstante zur Lösung hinzu

= \frac{10}{11} x^{\frac{11}{10}} + \frac{11}{12} x^{\frac{12}{11}} + C

\int \frac{sin ^{2} ( \frac{1}{t} )}{t ^{2}} d t

n = 0 \sum \infty (- 5 x)^{n}

\frac{d}{d t} ((\frac{t ^{3}}{4} - 2) + (\frac{4}{t} - 3) + cos (t - 2))

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

x \to 1 lim (5 x^{4} - 5 x^{2} + 10)