integral of (1+16x)/(sqrt(25-x^2))

Lösung

\int \frac{1 + 16 x}{25 - x ^{2}} d x

(1 + 16 x) arcsin (\frac{1}{5} x) - 16 (x arcsin (\frac{x}{5}) + 25 - x^{2}) + C

Schritte zur Lösung

\int \frac{1 + 16 x}{25 - x ^{2}} d x

Wende die partielle Integration an

= (1 + 16 x) arcsin (\frac{1}{5} x) - \int 16 arcsin (\frac{1}{5} x) d x

\int 16 arcsin (\frac{1}{5} x) d x = 16 (x arcsin (\frac{x}{5}) + 25 - x^{2})

= (1 + 16 x) arcsin (\frac{1}{5} x) - 16 (x arcsin (\frac{x}{5}) + 25 - x^{2})

Füge eine Konstante zur Lösung hinzu

= (1 + 16 x) arcsin (\frac{1}{5} x) - 16 (x arcsin (\frac{x}{5}) + 25 - x^{2}) + C

x \to 7 lim ((x^{2} - 49) (\frac{( x - 7 )}{∣ x - 7 ∣}))

\frac{d}{d x} (6 x + x)

\int \frac{2}{x 9 - x ^{2}} d x

x \to 0 - lim (\frac{1}{0})

t an g e n t f (x) = \frac{( 10 x )}{x ^{2} - 6}, at x = 4