Answer to Question #332667 in Calculus for Olga

Question

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

Answer 1

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

$\int F(x)dx=0.5\smallint x(\sqrt{x}+3\sqrt{x^3})dx=0.5\int (3x^{5/2}+x^{3/2})dx=\frac{3x^{7/2}}{7}+\frac{x^{5/2}}{5}+C$