integral of xsqrt(81+x^2)

Lösung

\int x 81 + x^{2} d x

\frac{1}{3} (81 + x^{2})^{\frac{3}{2}} + C

Schritte zur Lösung

\int x 81 + x^{2} d x

Wende U-Substitution an

= \int u^{2} d u

Wende die Potenzregel an

= \frac{u ^{3}}{3}

Setze in

u = 81 + x^{2}

ein

= \frac{( 81 + x ^{2} ) ^{3}}{3}

Vereinfache

\frac{( 81 + x ^{2} ) ^{3}}{3} : \frac{1}{3} (81 + x^{2})^{\frac{3}{2}}

= \frac{1}{3} (81 + x^{2})^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (81 + x^{2})^{\frac{3}{2}} + C

a re a y = 2 x, y = 12 - x, y = 4 - x

t an g e n t f (x) = \frac{2 x - 1}{x + 9}, at x = 2

d er i v a t i v e y = arccsc (4 x)

x y^{^{''}} + 2 y^{^{'}} = 8 x^{2}

\frac{\partial}{\partial y} (x e^{x y^{2}})