∫$$x51+x32/3dx=A1+x38/3+B1+x35/3+c$$ , then

Question

∫$$x51+x32/3dx=A1+x38/3+B1+x35/3+c$$ , then

Infinity Learn · Accepted Answer

Let $$1+x3=t2$$ ⇒ $$3x2dx=2tdt$$∴ ∫$$x51+x32/3dx=$$∫$$x31+x32/3x2dx$$                                           $$=$$∫$$t2$$−$$1t22/3x2dx$$                                           $$=23$$∫$$t2$$−$$1t7/3dt$$                                          $$=23$$∫$$t13/3$$−$$t7/3dt$$                                          $$=23316t163$$−$$310t10/3+c$$                                         $$=181+x38/3$$−$$151+x35/3+c$$

$\int x^{5} {(1 + x^{3})}^{2 / 3} d x = A {(1 + x^{3})}^{8 / 3} + B {(1 + x^{3})}^{5 / 3} + c, then$

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∫x51+x32/3dx=A1+x38/3+B1+x35/3+c , then

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$\int x^{5} {(1 + x^{3})}^{2 / 3} d x = A {(1 + x^{3})}^{8 / 3} + B {(1 + x^{3})}^{5 / 3} + c, then$