integral of 4x^2+2+5/(x^2+1)

Lösung

\int 4 x^{2} + 2 + \frac{5}{x ^{2} + 1} d x

\frac{4 x ^{3}}{3} + 2 x + 5 arctan (x) + C

Schritte zur Lösung

\int 4 x^{2} + 2 + \frac{5}{x ^{2} + 1} 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^{2} d x + \int 2 d x + \int \frac{5}{x ^{2} + 1} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 2 d x = 2 x

\int \frac{5}{x ^{2} + 1} d x = 5 arctan (x)

= \frac{4 x ^{3}}{3} + 2 x + 5 arctan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{4 x ^{3}}{3} + 2 x + 5 arctan (x) + C

\frac{\partial}{\partial t} (3 arcsin (t))

t an g e n t (x^{2} + y^{2})^{2} = 4 x^{2} y, (- 1, 1)

\int_{1}^{10} \frac{x ^{2} - 1}{x} d x

\frac{d}{d x} (\frac{2}{x - 3})

\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{3})