integral of (x^2+60)/(x^2+64)

Lösung

\int \frac{x ^{2} + 60}{x ^{2} + 64} d x

- \frac{1}{2} arctan (\frac{x}{8}) + x + C

Schritte zur Lösung

\int \frac{x ^{2} + 60}{x ^{2} + 64} d x

\frac{x ^{2} + 60}{x ^{2} + 64} = - \frac{4}{x ^{2} + 64} + 1

= \int - \frac{4}{x ^{2} + 64} + 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{4}{x ^{2} + 64} d x + \int 1 d x

\int \frac{4}{x ^{2} + 64} d x = \frac{1}{2} arctan (\frac{x}{8})

\int 1 d x = x

= - \frac{1}{2} arctan (\frac{x}{8}) + x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} arctan (\frac{x}{8}) + x + C

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

\int 5 e^{- x} d x

\int \frac{10 y + 11}{4 y ^{2} - 4 y + 5} d y

\int x^{2} e x^{3} d x

\int 2 (5^{x}) d x