Question

Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F. f(x) = 5 - 3(1 + x^2)^{-1}, F(1) = 0 F(x) = 5x - 3 arctan(x) + C

          Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F.

f(x) = 5 - 3(1 + x^2)^{-1}, F(1) = 0

F(x) = 5x - 3 arctan(x) + C

Added by Carly P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman K

05/09/2022

Step 1

Step 1:** Find the antiderivative of the function \(f(x) = 5 - 3(1 + x^2)^{-1}\): \[F(x) = \int (5 - 3(1 + x^2)^{-1}) dx\] \[F(x) = \int (5 - 3(1 + x^2)^{-1}) dx\] \[F(x) = \int 5 dx - \int 3(1 + x^2)^{-1} dx\] \[F(x) = 5x - 3 \int (1 + x^2)^{-1} dx\] ** Show more…

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Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F. f(x) = 5 - 3(1 + x^2)^-1, F(1) = 0 F(x) = 5x - 3 arctan(x) + C