I am having a hard time with this integral question. Can someone show me how to do this. Thank you.
Evaluate the indefinate integral
x^2(3x-1)dx
expand it to get
3x^3 - x^2
now you should have no difficulty integrating this.
To evaluate the indefinite integral of the expression x^2(3x-1)dx, we can use the method of integration known as expansion/FOIL.
Step 1: Expand the expression (3x-1) using the distributive property.
x^2(3x-1) = 3x^3 - x^2
Step 2: Distribute the x^2 to each term.
Integral x^2(3x-1)dx = Integral (3x^3 - x^2)dx
Step 3: Integrate each term separately.
Integral 3x^3dx - Integral x^2dx
Step 4: To integrate x^n, we add 1 to the power (n+1) and divide by the new power.
Integral 3x^3dx = (3/4)x^4 + C
Step 5: For the integral of x^2dx, we apply the same rule.
Integral x^2dx = (1/3)x^3 + C
Step 6: Combine the integrals by adding the constant of integration C.
Integral (3x^3 - x^2)dx = (3/4)x^4 + (1/3)x^3 + C
So, the indefinite integral of x^2(3x-1)dx is given by (3/4)x^4 + (1/3)x^3 + C, where C is the constant of integration.