integral of (sin(x)-2e^x+3sqrt(x))

Lösung

\int (sin (x) - 2 e^{x} + 3 x) d x

- cos (x) - 2 e^{x} + 2 x^{\frac{3}{2}} + C

Schritte zur Lösung

\int sin (x) - 2 e^{x} + 3 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 sin (x) d x - \int 2 e^{x} d x + \int 3 x d x

\int sin (x) d x = - cos (x)

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

\int 3 x d x = 2 x^{\frac{3}{2}}

= - cos (x) - 2 e^{x} + 2 x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= - cos (x) - 2 e^{x} + 2 x^{\frac{3}{2}} + C

\int y^{2} (\frac{1}{y ^{5}} + \frac{y ^{4}}{2}) d y

d er i v a t i v e 6 x arcsin (x)

d er i v a t i v e (t + e^{t}) (9 - t)

3 y^{^{'''}} + 12 y^{^{''}} + 12 y^{^{'}} = 0

\int_{0}^{1} (x^{2} + x) e^{x} d x