Question

integration (3x-2) (x-3) dx​

Answer 1

Step-by-step explanation:

(3x-2)(x-3)

3x(x-3)-2(x-3)

3x^2-9x-2x-6

3x^2-11x-6

Answer 2

Answer:

The answer for integration $(3x-2)(x-3)dx$ is $x^{3} -\frac{11}{2} x^{2} +6x+c$

Step-by-step explanation:

The question is to find the value of ∫ $(3x-2)(x-3)dx$. To find the answer, firstly we are going to open the bracket and rewrite the equation. Then we will get as follows,

∫$(3x-2)(x-3)dx=$∫$(3x^{2} -9x-2x+6)dx=$∫$(3x^{2} -11x+6)dx$

Now we are going to integrate every part in this equation. For integrating this, we are using the form ∫$x^ndx=\frac{x^{n+1} }{n+1}$ . Then,

∫$(3x^{2} -11x+6)dx=$∫$3x^{2}dx-$ ∫$11xdx$ $+$ ∫$6 dx$                

                          $=\frac{3x^{3} }{3}-\frac{11}{2} x^{2} +6x+c$

                         

So the final answer is ∫$(3x-2)(x-3)dx=x^{3} -\frac{11}{2} x^{2} +6x+c$

Thank you.