Evaluate the integrals in Exercises 31–78.
43. ∫tan(ln v...

Question

Evaluate the integrals in Exercises 31–78.

43. ∫tan(ln v)/v dv

Accepted Answer

Welcome back everyone. Evaluate the integral of cosine of square root of X divided by square root of X with respect to X. For this problem we're going to use substitution. Let's suppose that u is equal to the square root of x. Let's remember that the next step is to find the derivative of u with respect to x, and that's the derivative of the square root of x, which is 1 divided by 2 square root of x. Now what we can do is simply rearrange this expression for dx divided by the square root of x, so we can multiply both sides by dx, right? And we can also multiply both sides by 2, so that we get 2 multiplied by duu. Is equal to dx divided by the square root of x. Well done. So now we can rewrite our integral in terms of U and DU. We get cosine of u multiplied by dx divided by the square root of X, which is 2DU. We can now factor out the constant and notice that we're integrating cosine of u. Do you And now the integral of cosine is sine, so we are going to get to sine of u plus a constant of integration c since this is an indefinite integral. And finally, because u is square root of x, we get to sign. Of the square root of x + c, which is our final answer for this problem. Thank you for watching.

Evaluate the integrals in Exercises 31–78.43. ∫tan(ln v)/v dv

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Evaluate the integrals in Exercises 31–78.
43. ∫tan(ln v)/v dv