5

Rewrite the given integral using this substitution.dxLdu4144...

Question

Rewrite the given integral using this substitution.dxLdu4144

Rewrite the given integral using this substitution. dx L du 4144



Answers

Use substitution to evaluate the integral. $$\int \frac{d x}{x \ln x}$$

Let's start off here by just factoring the denominator. So we pull out of X and then let's do it. Use up here, you equals ln that do you is one over x gx so we can write this in a girl is one over humanise one, Do you? They do. You is equal to one over x t x. So that's taking care of this part right here, Phil. And then the U minus. Juan is taking care of the Ellen minus one. Now this we could integrate. That's just natural log. You minus one. Plus he now, if this minus one was bothering you, you can do it. A substitution here and you'LL arrive at this answer and then natural log. And finally, just come back up here and replace you with natural log of X. So we have natural lot Absolute value. Natural log X minus one closer constancy. And that's our final answer.

In there in Dickerson. Off sign hyperbolic function. Ah, we can solve this question by two. Mattered as we know. Sign Hyperbolic X Acquitted. Yes, minus minus. So ah, if well difference it this for different station off sign. Hyperbolic X will be yes, minus. It will be plus T minus x by two. Which is cause hyperbolic accident treatments. Difference. Ation off shine. Hyperbole. Benson It's cause have now, uh, come to the question excess Glad I see as they break consent if we treat them and integration off Sign hyperbole PX minus ESCWA is two x An integration off sign Hyperbolic X PX and hold dear. So come the ever detail. We can see all part as excess square invigoration off sign hyperbolic it men's despot Integration will be Obviously it is cause So it is because hyper bullet that's minus X it is two X and integration of sign happened. Bullet X is cause Have public X here. So excess where of course, hyperbolic minus do now again, we will use here by parse. So final part will be like i e Quito excess Glenn cause hyperbolic x finest. Now again, I'm using by parts. So exercise our site integration. Off course. Hyperbolic STX minus X definition is one. And in Dickerson, off course hyperbole. Now look at this question again. Will get shine. Hyperbolic X. Yeah, maybe it's Lexus Square, because hyperbolic X minus two X and this is sign hyperbolic X. Blessed to course, hyperbolic stew, this is

Okay, We've been given use excused in this problem, which means that we have 1/3 do you is equivalent to back squared DX. Which means that now we can pull out the constant one. Third time's the integral of Edith eu. Do you remember the integral of off? Either the U. S. Simply eat of the you. So now we're at the plant Will weaken back substitute and X squared expert Jax and we have our solution.

And I'll let you be L n X. And dvB X to the minus five dx. So do you want over x. Dx VX to the -4/-4 Or -1 or four X to the 4th. So we get u v minus one. Fourth over minus one minus 1/4 X. To the fourth times L n x minus the integral VD you. Which makes plus 1/4 X to the -5 DX. Okay, so minus 1/4 X. To the four L n x Plus 1 4th x to the -4/-4 plus T. So minus 1/4 X to the fourth. L n x -1/16 x to the fore plus C.


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