integral of e^x+x^e+e+x

Lösung

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

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

Schritte zur Lösung

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

\int e^{x} d x = e^{x}

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

\int e d x = e x

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

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e f (x) = sin (4 x) - cos (3 x)

\frac{d y}{d x} = x^{3} + x^{2} - 5 x + 11

\int_{1}^{1000} \frac{21}{x ^{3}} d x

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{t} cos (2 t)

l a pl a ce t r an s f or m (sin (6 t) - 7)^{2}