Question

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

Answer 1

Answer:

F(x)= 5*[$\frac{x^{3} }{3}$ + (a*b)*$\frac{x^{2} }{2}$ + a*b*x + C.

Step-by-step explanation:

First step we aplicate distributive property to the function.

5*(x+a)*(x+b)= 5*[$x^{2}$+x*b+a*x+a*b]

5*[$x^{2}$+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*[$x^{2}$+x*(a+b)+a*b]*dx, apply integral´s property

5*[∫$x^{2}$dx+∫(a*b)*x*dx + ∫a*b*dx], resolving the integrals

5*[$\frac{x^{3} }{3}$ + (a*b)*$\frac{x^{2} }{2}$ + a*b*x

Finally we can write the function F(x)

F(x)= 5*[$\frac{x^{3} }{3}$ + (a*b)*$\frac{x^{2} }{2}$ + a*b*x ]+ C.