∫(a13−x13)3dx=∫(a−3a23x13+3a13x23−x3)dx=\int \left(a^{\frac{1}{3}}-x^{\frac{1}{3}}\right)^3dx=\int(a-3a^{\frac{2}{3}}x^{\frac{1}{3}}+3a^{\frac{1}{3}}x^{\frac{2}{3}}-x^3)dx=∫(a31−x31)3dx=∫(a−3a32x31+3a31x32−x3)dx=
=ax−3a23x13+113+1+3a13x23+123+1−x44+C==ax-3a^{\frac{2}{3}}\frac{x^{\frac{1}{3}+1}}{\frac{1}{3}+1}+3a^{\frac{1}{3}}\frac{x^{\frac{2}{3}+1}}{\frac{2}{3}+1}-\frac{x^4}{4}+C==ax−3a3231+1x31+1+3a3132+1x32+1−4x4+C=
=ax−3a23x4343+3a13x5353−x44+C==ax-3a^{\frac{2}{3}}\frac{x^{\frac{4}{3}}}{\frac{4}{3}}+3a^{\frac{1}{3}}\frac{x^{\frac{5}{3}}}{\frac{5}{3}}-\frac{x^4}{4}+C==ax−3a3234x34+3a3135x35−4x4+C=
=ax−94a23xx13+95a13xx23−x44+C=ax-\frac{9}{4}a^{\frac{2}{3}}xx^{\frac{1}{3}}+\frac{9}{5}a^{\frac{1}{3}}xx^{\frac{2}{3}}-\frac{x^4}{4}+C=ax−49a32xx31+59a31xx32−4x4+C
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