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Evaluate:$$int frac{2-x^3}{(1+x^3)^{3/2}} dx$$I could find the integral by setting it equal to $$frac{ax+b}{(1+x^3)^{1/2}}$$and differentiating both sides w.r.t.$x$ as$$frac{2-x^3}{(1+x^3)^{3/2}}=frac{a(1+x^3)^{3/2}-(1/2)(ax+b)3x^2(1+x^3)^{-1/2}}{(1+x^3)}$$$$=frac{a-ax^3/2-3bx^2}{(1+x^3)^{3/2}}$$Finally by setting ...
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