integral of-2/(sqrt(7-7x^2))

Lösung

\int - \frac{2}{7 - 7 x ^{2}} d x

- 2 (\frac{x}{7 - 7 x ^{2}} - \frac{1}{7} (- arcsin (x) + \frac{x}{1 - x ^{2}})) + C

Schritte zur Lösung

\int - \frac{2}{7 - 7 x ^{2}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int \frac{1}{7 - 7 x ^{2}} d x

Wende die partielle Integration an

= - 2 (\frac{x}{7 - 7 x ^{2}} - \int \frac{7 x ^{2}}{( 7 - 7 x ^{2} ) ^{\frac{3}{2}}} d x)

\int \frac{7 x ^{2}}{( 7 - 7 x ^{2} ) ^{\frac{3}{2}}} d x = \frac{1}{7} (- arcsin (x) + \frac{x}{1 - x ^{2}})

= - 2 (\frac{x}{7 - 7 x ^{2}} - \frac{1}{7} (- arcsin (x) + \frac{x}{1 - x ^{2}}))

Füge eine Konstante zur Lösung hinzu

= - 2 (\frac{x}{7 - 7 x ^{2}} - \frac{1}{7} (- arcsin (x) + \frac{x}{1 - x ^{2}})) + C

\frac{d}{d x} (5 x^{3} - 3 x^{5})

t \to - 2 lim ((t + 4)^{2})

x \to - 1 lim (5 x^{2})

x y + y^{^{'}} = 64 x

t an g e n t f (x) = x^{2} + x, at x = 1