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Beliebt Rechnen >

integral of (2x+7)(x^2+7x+1)

Lösung

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

Lösung

\frac{2 x ^{4}}{3} - \frac{x ^{4}}{6} + 7 x^{3} + x^{2} + \frac{49 x ^{2}}{2} + 7 x + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{2 x ^{4}}{3} + 7 x^{3} + 2 x^{2} + \frac{7 x ^{3}}{3} + \frac{49 x ^{2}}{2} + 7 x - \int \frac{2 x ^{3}}{3} + 7 x^{2} + 2 x d x

\int \frac{2 x ^{3}}{3} + 7 x^{2} + 2 x d x = \frac{x ^{4}}{6} + \frac{7 x ^{3}}{3} + x^{2}

= \frac{2 x ^{4}}{3} + 7 x^{3} + 2 x^{2} + \frac{7 x ^{3}}{3} + \frac{49 x ^{2}}{2} + 7 x - (\frac{x ^{4}}{6} + \frac{7 x ^{3}}{3} + x^{2})

Vereinfache

\frac{2 x ^{4}}{3} + 7 x^{3} + 2 x^{2} + \frac{7 x ^{3}}{3} + \frac{49 x ^{2}}{2} + 7 x - (\frac{x ^{4}}{6} + \frac{7 x ^{3}}{3} + x^{2}) : \frac{2 x ^{4}}{3} - \frac{x ^{4}}{6} + 7 x^{3} + x^{2} + \frac{49 x ^{2}}{2} + 7 x

= \frac{2 x ^{4}}{3} - \frac{x ^{4}}{6} + 7 x^{3} + x^{2} + \frac{49 x ^{2}}{2} + 7 x

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{4}}{3} - \frac{x ^{4}}{6} + 7 x^{3} + x^{2} + \frac{49 x ^{2}}{2} + 7 x + C

Graph

Beliebte Beispiele

integral of ((6x-5))/(sqrt(3x^2-5x+6))

\int \frac{( 6 x - 5 )}{3 x ^{2} - 5 x + 6} d x

integral of ((x^3)/3+2)^2x^3

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

integral of sqrt(3^2-x^2)

\int 3^{2} - x^{2} d x

integral of x/(3+x^4)

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

integral of (x^2+22)/(x^2+25)

\int \frac{x ^{2} + 22}{x ^{2} + 25} d x