integral of \sqrt[4]{x}+1/(\sqrt[4]{x)}

Lösung

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

\frac{4}{5} x^{\frac{5}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

Schritte zur Lösung

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

\int 4 x d x = \frac{4}{5} x^{\frac{5}{4}}

\int \frac{1}{4 x} d x = \frac{4}{3} x^{\frac{3}{4}}

= \frac{4}{5} x^{\frac{5}{4}} + \frac{4}{3} x^{\frac{3}{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{5} x^{\frac{5}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

\int 5 x e^{- 2 x} d x

in v erse l a pl a ce \frac{2}{s + 3}

in v erse l a pl a ce \frac{s + 1}{( s ^{2} + 9 )}

t an g e n t f (x) = 2 x^{2} - 3 x - 2, at x = 6

\int_{- \infty}^{- 1} e^{- 4 t} d t