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Determine the antiderivative of 1/(x+5)
Solution
We'll calculate the antiderivative F(x) integrating the given function.
F(x) is a function such as dF/dx = f(x).
Int f(x)dx = F(x) + C
Int dx/(x+5)
We'll substitute the denominator of the function by another variable:
x + 5 = t
We'll differentiate both sides:
(x+5)'dx = dt
dx = dt
We'll re-write the indefinite integral using the variable t:
Int dt/t = ln |t| + C
We'll substitute t by the expression in x:
F(x) = ln |x+5| + C
The antiderivative of the function y = 1/(x+5) is F(x)=ln |x+5| + C.

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Determine the antiderivative of 1(x+5)SolutionWell calculat.pdf

  • 1. Determine the antiderivative of 1/(x+5) Solution We'll calculate the antiderivative F(x) integrating the given function. F(x) is a function such as dF/dx = f(x). Int f(x)dx = F(x) + C Int dx/(x+5) We'll substitute the denominator of the function by another variable: x + 5 = t We'll differentiate both sides: (x+5)'dx = dt dx = dt We'll re-write the indefinite integral using the variable t: Int dt/t = ln |t| + C We'll substitute t by the expression in x: F(x) = ln |x+5| + C The antiderivative of the function y = 1/(x+5) is F(x)=ln |x+5| + C.