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
F(x)=x12(x+3x3)F(x)=x\frac{1}{2}(\sqrt{x}+3\sqrt {x^3})F(x)=x21(x+3x3)
∫F(x)dx=0.5∫x(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∫F(x)dx=0.5∫x(x+3x3)dx=0.5∫(3x5/2+x3/2)dx=73x7/2+5x5/2+C
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