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Beliebt Rechnen >

integral of ((x^2+3x+4)^2)/(sqrt(x))

Lösung

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

Lösung

\frac{2}{9} x^{\frac{9}{2}} + \frac{12}{7} x^{\frac{7}{2}} + \frac{34}{5} x^{\frac{5}{2}} + 16 x^{\frac{3}{2}} + 32 x + C

Schritte zur Lösung

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

Multipliziere aus

\frac{( x ^{2} + 3 x + 4 ) ^{2}}{x} : x^{\frac{7}{2}} + 6 x^{\frac{5}{2}} + 17 x^{\frac{3}{2}} + 24 x + \frac{16}{x}

= \int x^{\frac{7}{2}} + 6 x^{\frac{5}{2}} + 17 x^{\frac{3}{2}} + 24 x + \frac{16}{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 x^{\frac{7}{2}} d x + \int 6 x^{\frac{5}{2}} d x + \int 17 x^{\frac{3}{2}} d x + \int 24 x d x + \int \frac{16}{x} d x

\int x^{\frac{7}{2}} d x = \frac{2}{9} x^{\frac{9}{2}}

\int 6 x^{\frac{5}{2}} d x = \frac{12}{7} x^{\frac{7}{2}}

\int 17 x^{\frac{3}{2}} d x = \frac{34}{5} x^{\frac{5}{2}}

\int 24 x d x = 16 x^{\frac{3}{2}}

\int \frac{16}{x} d x = 32 x

= \frac{2}{9} x^{\frac{9}{2}} + \frac{12}{7} x^{\frac{7}{2}} + \frac{34}{5} x^{\frac{5}{2}} + 16 x^{\frac{3}{2}} + 32 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{9} x^{\frac{9}{2}} + \frac{12}{7} x^{\frac{7}{2}} + \frac{34}{5} x^{\frac{5}{2}} + 16 x^{\frac{3}{2}} + 32 x + C

Graph

Beliebte Beispiele

integral of 2cos(4x)cos(9x)

\int 2 cos (4 x) cos (9 x) d x

integral of 1/(16x^2-24x-7)

\int \frac{1}{16 x ^{2} - 24 x - 7} d x

integral of 1/(cos(4θ))

\int \frac{1}{cos ( 4 θ )} d θ

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

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

integral of (5x^4-10)/(x^6)

\int \frac{5 x ^{4} - 10}{x ^{6}} d x