integral of (1+u+u^2+u^5)

Lösung

\int (1 + u + u^{2} + u^{5}) d u

u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3} + \frac{u ^{6}}{6} + C

Schritte zur Lösung

\int 1 + u + u^{2} + u^{5} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u + \int u d u + \int u^{2} d u + \int u^{5} d u

\int 1 d u = u

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

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

\int u^{5} d u = \frac{u ^{6}}{6}

= u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3} + \frac{u ^{6}}{6}

Füge eine Konstante zur Lösung hinzu

= u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3} + \frac{u ^{6}}{6} + C

\int \frac{1}{x ln ( x ) + x} d x

\int (y^{2} - y^{3}) d y

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

\int \frac{cos ( z )}{1 + sin ( z )} d z

\int 0.2 x + 1 d x