Evaluate the integral. (assume a ≠ b. remember to use absolute values where appropriate. use c for the constant of integration.) 5 (x + a)(x + b) dx

F(x)= 5*[ + (a*b)* + a*b*x + C.

Step-by-step explanation:

First step we aplicate distributive property to the function.

5*(x+a)*(x+b)= 5*[+x*b+a*x+a*b]

5*[+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*[+x*(a+b)+a*b]*dx, apply integral´s property

5*[∫dx+∫(a*b)*x*dx + ∫a*b*dx], resolving the integrals

5*[ + (a*b)* + a*b*x

Finally we can write the function F(x)

F(x)= 5*[ + (a*b)* + a*b*x ]+ C.

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step-by-step explanation: