integral of (2x-5)^{11}

Lösung

\int (2 x - 5)^{11} d x

(2 x - 5)^{11} x - 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2}) + C

Schritte zur Lösung

\int (2 x - 5)^{11} d x

Wende die partielle Integration an

= (2 x - 5)^{11} x - \int 22 (2 x - 5)^{10} x d x

\int 22 (2 x - 5)^{10} x d x = 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2})

= (2 x - 5)^{11} x - 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= (2 x - 5)^{11} x - 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2}) + C

\int_{- 1}^{2} \frac{x}{( x + 1 ) ^{2}} d x

x^{^{'}} = 6 c_{1} - \frac{3 x}{5}

\int_{0}^{1} x (1 - x^{2}) d x

f (t) = \frac{t ^{2}}{2}

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