Evaluate the integrals in Exercises 33–54.
∫ (e^(1/x) / ...

Question

Evaluate the integrals in Exercises 33–54.

∫ (e^(1/x) / x²) dx

Accepted Answer

Welcome back everyone. Evaluate the integral of e to the power of 5 divided by x divided by x 2 dx. We're going to approach this problem using U substitution. Let's suppose that U is equal to 5 divided by x. Let's remember that our next step is to find the derivative of you with respect to x. So that's the derivative of 5 divided by x. We can find it by. Multiplying 5 by the derivative of x to the power of -1, right? And here we can apply the power rule which gives us -5, x to the power of -2, or basically -5 divided by x 2. Now, what we can notice is that our integral contains dx divided by x2. So we can rearrange this relationship and we can show that DU is equal to -5 divided by x2DX. And now let's divide both sides by -5, which gives us 1/5. DU equals dx divided by x2, which allows us to rewrite the integral in terms of U and DU. So now the integral becomes E to the power of u multiplied by d x divided by x squared, which is -15 duu. We can write d u and we can factor out 1/5. And now we have an elementary integral. We're going to write our constant -15. And the integral of eats the power of u is eats the power of u plus a constant of integration c because we have an indefinite integral. And finally replacing you with 55 divided by x. We're going to get -1/5 e to the power of 5 divided by x. Plus a constant of integration c and that's our final answer for this problem. Thank you for watching.

Evaluate the integrals in Exercises 33–54.∫ (e^(1/x) / x²) dx

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Evaluate the integrals in Exercises 33–54.
∫ (e^(1/x) / x²) dx