integral of xsqrt(5/2x^2+7)

Lösung

\int x \cdot \frac{5}{2} \cdot x^{2} + 7 d x

\frac{1}{2 2} x^{2} 5 x^{2} + 14 - \frac{1}{30 2} ((5 x^{2} + 14)^{\frac{3}{2}} - 42 5 x^{2} + 14) + C

Schritte zur Lösung

\int x \frac{5}{2} x^{2} + 7 d x

Wende die partielle Integration an

= \frac{1}{2 2} x^{2} 5 x^{2} + 14 - \int \frac{5 x ^{3}}{2 2 5 x ^{2} + 14} d x

\int \frac{5 x ^{3}}{2 2 5 x ^{2} + 14} d x = \frac{1}{30 2} ((5 x^{2} + 14)^{\frac{3}{2}} - 42 5 x^{2} + 14)

= \frac{1}{2 2} x^{2} 5 x^{2} + 14 - \frac{1}{30 2} ((5 x^{2} + 14)^{\frac{3}{2}} - 42 5 x^{2} + 14)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2 2} x^{2} 5 x^{2} + 14 - \frac{1}{30 2} ((5 x^{2} + 14)^{\frac{3}{2}} - 42 5 x^{2} + 14) + C

\int_{0}^{2} 2^{- x} d x

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y})

x \to 0 lim (2 (1 + 3 x)^{\frac{2}{x}})

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{4 x - 2})

ma c l a u r in ln (3 + x)