integral of 5x^3+e^x-cos(x)

Lösung

\int 5 x^{3} + e^{x} - cos (x) d x

\frac{5 x ^{4}}{4} + e^{x} - sin (x) + C

Schritte zur Lösung

\int 5 x^{3} + e^{x} - cos (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 5 x^{3} d x + \int e^{x} d x - \int cos (x) d x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

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

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

= \frac{5 x ^{4}}{4} + e^{x} - sin (x)

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{4}}{4} + e^{x} - sin (x) + C

\int \frac{x ^{2} + 4 x + 2}{x ^{2} + 1} d x

\int \frac{e ^{\frac{1}{x}}}{5 x ^{2}} d x

\int \frac{7 sin ( x )}{1 + cos ^{2} ( x )} d x

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

\int \frac{1}{p ^{3}} d p