Answer:
F(x)= 5*[[tex]\frac{x^{3} }{3}[/tex] + (a*b)*[tex]\frac{x^{2} }{2}[/tex] + a*b*x + C.
Step-by-step explanation:
First step we aplicate distributive property to the function.
5*(x+a)*(x+b)= 5*[[tex]x^{2}[/tex]+x*b+a*x+a*b]
5*[[tex]x^{2}[/tex]+x*(b+a)+a*b]= f(x), where a, b are constant and a≠b
integrating we find ⇒∫f(x)*dx= F(x) + C, where C= integration´s constant
∫^5*[[tex]x^{2}[/tex]+x*(a+b)+a*b]*dx, apply integral´s property
5*[∫[tex]x^{2}[/tex]dx+∫(a*b)*x*dx + ∫a*b*dx], resolving the integrals
5*[[tex]\frac{x^{3} }{3}[/tex] + (a*b)*[tex]\frac{x^{2} }{2}[/tex] + a*b*x
Finally we can write the function F(x)
F(x)= 5*[[tex]\frac{x^{3} }{3}[/tex] + (a*b)*[tex]\frac{x^{2} }{2}[/tex] + a*b*x ]+ C.
