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Evaluate the following integrals: int (x^3 +3x +4)/sqrtx dx

Answer»

SOLUTION :`int (X^3+3x+4)/sqrtx DX = int (x^3/sqrtx + (3x)/sqrtx + 4/sqrtx) dx`
=`int(x^(3-1/2) +3sqrtx+4/sqrtx)dx = int(x^(5/2) + 3x^(1/2) +4/sqrtx) dx`
=`x^(5/2+1)/(5/2+1) +3x^(1/2+1)/(1/2+1) + 4xx2sqrtx+C`
=`x^(7/2)/(7/2) +(3x^3/2))/(3/20 + 8sqrtx +c = (2x^(7/2)/7 + 2x^93/2) + 8sqrtx+c`


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