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

t an g e n t f (x) = - 3 cos (x), at x = - \frac{π}{3}

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