integral of x^3+3^x+e^3

Lösung

\int x^{3} + 3^{x} + e^{3} d x

\frac{x ^{4}}{4} + \frac{3 ^{x}}{ln ( 3 )} + e^{3} x + C

Schritte zur Lösung

\int x^{3} + 3^{x} + e^{3} 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 x^{3} d x + \int 3^{x} d x + \int e^{3} d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

\int e^{3} d x = e^{3} x

= \frac{x ^{4}}{4} + \frac{3 ^{x}}{ln ( 3 )} + e^{3} x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + \frac{3 ^{x}}{ln ( 3 )} + e^{3} x + C

\int (- 3 x^{6} + 4 x^{5} + 4 x^{4} + 3) d x

\int (3 sin (y)) d y

\int x^{3} + x^{2} y d y

\int \frac{x ^{2}}{4} + \frac{3 x}{4} + 2 d x

\int x^{3} lo g_{e} (x) d x