Recall that if F(x) is an antiderivative of f(x), then so is any function of the form F(x) + C, where C is an arbitrary constant. Since we can use any antiderivative to evaluate the definite integral, it is easiest to use the antiderivative with a constant term of 0. It is not easy to directly find an antiderivative of f(x) = long division.) x²-9 1 + x² x2-9+1-1 1 + x² (x²+1) - 1 1+x² 1+x² x x²-9 1+x2' so we can algebraically manipulate it by adding and subtracting the number 1 in the numerator. (We get the same results if we perform It will be easier to find the antiderivative of f(x) in this form.

Recall that if F(x) is an antiderivative of f(x), then so is any function of the form F(x) + C, where C is an arbitrary constant. Since we can use any antiderivative to evaluate the definite integral, it is easiest to use the antiderivative with a constant term of 0. It is not easy to directly find an antiderivative of f(x) = long division.) x²-9 1 + x² x2-9+1-1 1 + x² (x²+1) - 1 1+x² 1+x² x x²-9 1+x2' so we can algebraically manipulate it by adding and subtracting the number 1 in the numerator. (We get the same results if we perform It will be easier to find the antiderivative of f(x) in this form.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 36E

See similar textbooks