Evaluate the integrals in Exercises 111–114.
112. ∫₁^(eˣ...

Question

Evaluate the integrals in Exercises 111–114.

112. ∫₁^(eˣ) (1 / t) dt

Accepted Answer

Welcome back, everyone. Evaluate the integral integral from 1 up to E to the power of 2 X + 1 of 1 divided by TDT. A 2 X + 1, B2 X C E to the power of 2 X + 1 minus 1, and D 2E to the power of X. For this problem, let's go ahead and rewrite the integral from 1 up to E to the power of 2 X plus 1 of 1 divided by TDC. First of all, we can integrate. This is an elementary integral, and we can conclude that the value is LN of the absolute value of T. And because we have a definite integral, we want to calculate the result from 1 up to E to the power of 2 X + 1. Let's apply the fundamental theorem of calculus part 2. We first of all take LN of the absolute value of E to the power of 2 X + 1. And we subtract a land of the absolute value of one. Now, what we can also do is simply drop each absolute value because Each is greater than 0, specifically one is greater than 0, and our exponential function is also greater than 0, right? And LN 1 is simply 0, so we can cancel it out and we can focus on LN of E to the power of 2 X plus 1. Using the properties of logarithms, we can bring down the exponent to get 2 X + 1 multiplied by LN of E, and because LN of E is equal to 1, we get 2 X plus 1, which is our final answer, and it corresponds to the answer choice A. Thank you for watching.

Evaluate the integrals in Exercises 111–114.112. ∫₁^(eˣ) (1 / t) dt

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Evaluate the integrals in Exercises 111–114.
112. ∫₁^(eˣ) (1 / t) dt