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Beliebt Rechnen >

integral of ((7+x^{2/3})^5)/(x^{1/3)}

Lösung

\int \frac{( 7 + x ^{\frac{2}{3}} ) ^{5}}{x ^{\frac{1}{3}}} d x

Lösung

\frac{50421}{2} x^{\frac{2}{3}} + \frac{36015}{4} x^{\frac{4}{3}} + 1715 x^{2} + \frac{735}{4} x^{\frac{8}{3}} + \frac{21}{2} x^{\frac{10}{3}} + \frac{x ^{4}}{4} + C

Schritte zur Lösung

\int \frac{( 7 + x ^{\frac{2}{3}} ) ^{5}}{x ^{\frac{1}{3}}} d x

Multipliziere aus

\frac{( 7 + x ^{\frac{2}{3}} ) ^{5}}{x ^{\frac{1}{3}}} : \frac{16807}{x ^{\frac{1}{3}}} + 12005 x^{\frac{1}{3}} + 3430 x + 490 x^{\frac{5}{3}} + 35 x^{\frac{7}{3}} + x^{3}

= \int \frac{16807}{x ^{\frac{1}{3}}} + 12005 x^{\frac{1}{3}} + 3430 x + 490 x^{\frac{5}{3}} + 35 x^{\frac{7}{3}} + x^{3} 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 \frac{16807}{x ^{\frac{1}{3}}} d x + \int 12005 x^{\frac{1}{3}} d x + \int 3430 x d x + \int 490 x^{\frac{5}{3}} d x + \int 35 x^{\frac{7}{3}} d x + \int x^{3} d x

\int \frac{16807}{x ^{\frac{1}{3}}} d x = \frac{50421}{2} x^{\frac{2}{3}}

\int 12005 x^{\frac{1}{3}} d x = \frac{36015}{4} x^{\frac{4}{3}}

\int 3430 x d x = 1715 x^{2}

\int 490 x^{\frac{5}{3}} d x = \frac{735}{4} x^{\frac{8}{3}}

\int 35 x^{\frac{7}{3}} d x = \frac{21}{2} x^{\frac{10}{3}}

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

= \frac{50421}{2} x^{\frac{2}{3}} + \frac{36015}{4} x^{\frac{4}{3}} + 1715 x^{2} + \frac{735}{4} x^{\frac{8}{3}} + \frac{21}{2} x^{\frac{10}{3}} + \frac{x ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{50421}{2} x^{\frac{2}{3}} + \frac{36015}{4} x^{\frac{4}{3}} + 1715 x^{2} + \frac{735}{4} x^{\frac{8}{3}} + \frac{21}{2} x^{\frac{10}{3}} + \frac{x ^{4}}{4} + C

Graph

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