integral of ((x^2+3))/(x^2+1)

Lösung

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

2 arctan (x) + x + C

Schritte zur Lösung

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

\frac{x ^{2} + 3}{x ^{2} + 1} = \frac{2}{x ^{2} + 1} + 1

= \int \frac{2}{x ^{2} + 1} + 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 \frac{2}{x ^{2} + 1} d x + \int 1 d x

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

\int 1 d x = x

= 2 arctan (x) + x

Füge eine Konstante zur Lösung hinzu

= 2 arctan (x) + x + C

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

s l o p e (3, 8), (- 7, 7)

\int sin (2 x) e^{c o s (2)} x d x

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

\int_{0}^{1} e^{- 0.1 t} d t