integral of (x+1)(2x^2+sqrt(x))

Lösung

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

(x + 1) (\frac{2 x ^{3}}{3} + \frac{2}{3} x^{\frac{3}{2}}) - \frac{1}{3} (\frac{x ^{4}}{2} + \frac{4}{5} x^{\frac{5}{2}}) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= (x + 1) (\frac{2 x ^{3}}{3} + \frac{2}{3} x^{\frac{3}{2}}) - \int \frac{1}{3} (2 x^{3} + 2 x^{\frac{3}{2}}) d x

\int \frac{1}{3} (2 x^{3} + 2 x^{\frac{3}{2}}) d x = \frac{1}{3} (\frac{x ^{4}}{2} + \frac{4}{5} x^{\frac{5}{2}})

= (x + 1) (\frac{2 x ^{3}}{3} + \frac{2}{3} x^{\frac{3}{2}}) - \frac{1}{3} (\frac{x ^{4}}{2} + \frac{4}{5} x^{\frac{5}{2}})

Füge eine Konstante zur Lösung hinzu

= (x + 1) (\frac{2 x ^{3}}{3} + \frac{2}{3} x^{\frac{3}{2}}) - \frac{1}{3} (\frac{x ^{4}}{2} + \frac{4}{5} x^{\frac{5}{2}}) + C

d er i v a t i v e f (x) = x cos (x) + 2 tan (x)

\int coth (\frac{x}{3}) d x

\frac{d}{d x} (a \cdot e^{x})

n = 1 \sum \infty \frac{3}{n + 1}

d er i v a t i v e f (x) = sin (8 x + 4)