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
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![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
x²9
so we can algebraically manipulate it by adding and subtracting the number 1 in the numerator. (We get the same results if we perform
1 + x²
It will be easier to find the antiderivative of f(x) in this form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2065d956-6c8d-4dd3-a865-df08e0123eae%2Fc18ab90d-b813-42b3-abae-01b9d4a71ec1%2Fqbsyus_processed.png&w=3840&q=75)
Transcribed Image Text: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
x²9
so we can algebraically manipulate it by adding and subtracting the number 1 in the numerator. (We get the same results if we perform
1 + x²
It will be easier to find the antiderivative of f(x) in this form.
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