integral of ((e^x)/2+xsqrt(x))

Lösung

\int (\frac{e ^{x}}{2} + x x) d x

\frac{1}{2} e^{x} + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

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

\int \frac{e ^{x}}{2} d x = \frac{1}{2} e^{x}

\int x x d x = \frac{2}{5} x^{\frac{5}{2}}

= \frac{1}{2} e^{x} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} e^{x} + \frac{2}{5} x^{\frac{5}{2}} + C

y^{^{'}} = \frac{4 x ^{7} e ^{\frac{y}{x}} + x ^{5} y ^{2}}{x ^{6} y}

\frac{d}{d x} (\frac{sin ( x )}{ln ( x )})

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

y^{^{''}} - 8 y^{^{'}} + 16 = 0

x \to π lim ((π - x) cot (x))