integral of (15/8 x^7+2/7 x^2)^3

解

\int (\frac{15}{8} x^{7} + \frac{2}{7} x^{2})^{3} d x

\frac{3375 x ^{22}}{11264} + \frac{675 x ^{17}}{3808} + \frac{15 x ^{12}}{392} + \frac{8 x ^{7}}{2401} + C

解答ステップ

\int (\frac{15}{8} x^{7} + \frac{2}{7} x^{2})^{3} d x

拡張

(\frac{15}{8} x^{7} + \frac{2}{7} x^{2})^{3} : \frac{3375 x ^{21}}{512} + \frac{675 x ^{16}}{224} + \frac{45 x ^{11}}{98} + \frac{8 x ^{6}}{343}

= \int \frac{3375 x ^{21}}{512} + \frac{675 x ^{16}}{224} + \frac{45 x ^{11}}{98} + \frac{8 x ^{6}}{343} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{3375 x ^{21}}{512} d x + \int \frac{675 x ^{16}}{224} d x + \int \frac{45 x ^{11}}{98} d x + \int \frac{8 x ^{6}}{343} d x

\int \frac{3375 x ^{21}}{512} d x = \frac{3375 x ^{22}}{11264}

\int \frac{675 x ^{16}}{224} d x = \frac{675 x ^{17}}{3808}

\int \frac{45 x ^{11}}{98} d x = \frac{15 x ^{12}}{392}

\int \frac{8 x ^{6}}{343} d x = \frac{8 x ^{7}}{2401}

= \frac{3375 x ^{22}}{11264} + \frac{675 x ^{17}}{3808} + \frac{15 x ^{12}}{392} + \frac{8 x ^{7}}{2401}

定数を解答に追加する

= \frac{3375 x ^{22}}{11264} + \frac{675 x ^{17}}{3808} + \frac{15 x ^{12}}{392} + \frac{8 x ^{7}}{2401} + C