got as question

Question

Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

dx

2x + 7

Answer 1

integral of 2x +7

= (2x^2)/2 + 7x + c

= x^2 + 7x + c

integrate by increasing the exponent of each term by 1 and dividing by the same

2x with the increased exponent is 2x^2, then divide by 3 to get x^2

7 = 7x^0. increase 0 to 1 to get 7x^1 = 7x, then divide by 1 to get 7x

add them together x^2 +7x. then add c to get x^2 +7x + c

general formula is the integral of u^x = u^(x+1)/(x+1) + c

Had there been a term such as 1/x, you can't increase the exponent by 1 and divide by 0, so the integral is ln|x| +c, where you need the absolute value sign for the natural log. general formula is the integral of du/u = ln|u| + c