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Beliebt Rechnen >

integral of ((2+sqrt(x))^6)/(sqrt(x))

Lösung

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

Lösung

x (2 + x)^{6} - \frac{1}{7} (5 x^{\frac{7}{2}} + 252 x^{\frac{5}{2}} + 560 x^{\frac{3}{2}} + 56 x^{3} + 560 x^{2} - 448 x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{6 x ( x + 2 ) ^{5} - ( 2 + x ) ^{6}}{2 x} d x = \frac{1}{7} (5 x^{\frac{7}{2}} + 252 x^{\frac{5}{2}} + 560 x^{\frac{3}{2}} + 56 x^{3} + 560 x^{2} - 448 x)

= x (2 + x)^{6} - \frac{1}{7} (5 x^{\frac{7}{2}} + 252 x^{\frac{5}{2}} + 560 x^{\frac{3}{2}} + 56 x^{3} + 560 x^{2} - 448 x)

Füge eine Konstante zur Lösung hinzu

= x (2 + x)^{6} - \frac{1}{7} (5 x^{\frac{7}{2}} + 252 x^{\frac{5}{2}} + 560 x^{\frac{3}{2}} + 56 x^{3} + 560 x^{2} - 448 x) + C

Graph

Beliebte Beispiele

integral of 1/(2+4x^4)(16x^3)

\int \frac{1}{2 + 4 x ^{4}} (16 x^{3}) d x

integral of ((x^2-1)^3)/(sqrt(x))

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

integral of (x^2)/((x^2-16)^{5/2)}

\int \frac{x ^{2}}{( x ^{2} - 16 ) ^{\frac{5}{2}}} d x

integral of (1+cos(4x))^2

\int (1 + cos (4 x))^{2} d x

integral of (2+x^2)/x

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