Question #332667

Evaluate the following integral:

∫ [x 1 / 2 (√ x + 3√ x ^3) ] dx 

 


a.    X  + 2 / 3   x^3 / 2  + c 


b.   X ^ 2 / 2 + 2 / 5  x^5/2 + c


c.    X^2 / 2 + 5 / 2 x^ 5 / 2  + c 


d.   X  + x^ 3 / 2  + c



1
Expert's answer
2022-04-29T08:26:47-0400

F(x)=x12(x+3x3)F(x)=x\frac{1}{2}(\sqrt{x}+3\sqrt {x^3})

F(x)dx=0.5x(x+3x3)dx=0.5(3x5/2+x3/2)dx=3x7/27+x5/25+C\int F(x)dx=0.5\smallint x(\sqrt{x}+3\sqrt{x^3})dx=0.5\int (3x^{5/2}+x^{3/2})dx=\frac{3x^{7/2}}{7}+\frac{x^{5/2}}{5}+C



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