integral of 2sin(x)+2x^2+5x+1

Lösung

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

- 2 cos (x) + \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} + x + C

Schritte zur Lösung

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

\int 2 sin (x) d x = - 2 cos (x)

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 1 d x = x

= - 2 cos (x) + \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} + x

Füge eine Konstante zur Lösung hinzu

= - 2 cos (x) + \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} + x + C

\frac{d}{d x} (\frac{2 x - 3}{x ^{2}})

\int \frac{81 + x ^{2}}{x} d x

x \to \infty lim (3 x^{3} + 3 x^{2} - x)

\int \frac{6 - x}{6 + x} d x

n = 0 \sum \infty \frac{2 ^{n}}{1 ^{n}}