integrate-each-of-the-given-functions-int-fracsin-1-x2-x2-d-x-3

Question

Integrate each of the given functions.
$$\int \frac{\sin (1 / x)}{2 x^{2}} d x$$

Tyler Moulton · Accepted Answer

All right. We want to integrate the following integral. That is the indefinite integral of sine of one over X. D X divided by two X square. This question is testing our knowledge of methods of integration. We&#x27;ve previously learned about the power rule for integration, the log rule and the exponential role in this problem. We&#x27;re being challenged to use trigger metric integral. So there are 10 million metric integral. To identify which one we need to use. We need to identify which triggered metric function. President are integral matches with one of those one through 10. So we see that are integral has signed. Therefore we&#x27;re gonna use integral one which has solution negative coast you plus C. Therefore to use one effectively we have to identify you do you so you as one over X. The argument sign. Do you then is negative one over X squared dx. So are integral has an extra factor of negative two that we carry over to our final solution. So carrying over the negative to and including negative coast plus the other solution, we have our integral equal to four. Co sign one over X plus C.

Alex Johnson · Answer

this problem, We&#x27;re gonna find the anti derivative of X Sign of the corn. The X weird. This will be a U sub problems of First. Let&#x27;s assigning you value of X weird. And then we&#x27;ll take the derivative to find d&#x27;you, which will be two x d x. We&#x27;ll need to move the two over by divisions that we can do a proper substitution. And as we look at the original, you can see that the X squared here will be then replaced with you and then our our ex and then r D X will be replaced with 1/2 the U So are integral will look like this will have a 1/2 coefficient in front and then we replace our associated values here with sign of you D you and that are anti derivative is negative 1/2 co sign of you plus C and we substitute back to get the correct anti derivative with X. So we have negative 1/2 coastline of X squared plus C

Amit Srivastava · Answer

I equal to son was X by x esquire dear So investors, your first function the signing of us X as a you and one by access CWA as your DX minus different station off signed over sex DX integration off one by excess car DX and hold. It&#x27;s so final part will be sun inverse X and it is X minus. Studi X de physician off, Sandberg says, will be one minus X s part Integris an X minus two plus one. So here it will be plus are intimately 40. So signing worth X and it is X minus two. Blessed one by minus one. Bless one by axe handle one minus X squared. So final answer will be one bikes which minus saying sign birth sex less the X by X entitled one minus X squared. But is there direct integration? Off course Taken about six filler Just minus. Sign some minus one bikes sign in verse six minus cause it was Yes,

Foster Wisusik · Answer

Okay, This question wants us to integrate this function. So usually when you have trick functions, we pick you to be the argument off that function. So in our case, let&#x27;s pick you equal to two x squared. So this means that do you would be equal to four x d x, and we only have one X in are integral, So let&#x27;s divide each side by four. So this tells us that D&#x27;You over four is equal to for it&#x27;s a X d X. So now we can substitute into are integral. So we have the integral of sign of you times d&#x27;you divided by four. And that&#x27;s just 1/4 time&#x27;s the integral of sign of you Do you ends that works out to be negative on fourth co sign you plus C or converting back to X. We get negative. 1/4 co sign of you was two x squared plus C, and that&#x27;s our answer

Sid Wan · Answer

Okay. Lumber six with newt. Toe calculates integral to axe Kasai. Ax squared DX Sorry. We cannot orders prerogative of ex squares. Toe substitution do equals at square. Ah, the U equals two ax Teo. So he comes to you. That guy equals cause I you to you. Not this one. If you checked the four Miller is going to be fine. You pussy And you can substitute back sine x square, Plus it does it.

Robert Daugherty · Answer

Section seven Note to problem eight or asked to integrate the General x Times a sign of two X So an integration by parts you typically I&#x27;m gonna let it be the polynomial term. So D u is equal to D X. That should be easier to show up in an integral And then Devi is going to be going to the sign of two x dx. You integrate the sine function and you get minus the co sign functions or mine that&#x27;s co signed two X divided by two is going to be the V term. So this and grow is going to be UV minus the integral v d u. And I&#x27;m hoping that the integral VT you is something easier to work with. So this is going to be minus 1/2 X, um co sign two X and then minus the integral of Edie you So that&#x27;s gonna be 1/2 the integral co sign two x the X So this is minus 1/2 X go sign of two X. When you integrate the coastline function, you get the sine functions. That this is gonna be one fourth sign of two X plus constant of integration, and that is the final answer here

Problem

Integrate each of the given functions. $$\int \fr…

Problem 13 Easy Difficulty

Integrate each of the given functions.
$$\int \frac{\sin (1 / x)}{2 x^{2}} d x$$

Answer

$\frac{1}{2} \cos \left(\frac{1}{x}\right)+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Heather Z.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{1}{2} \cos \left(\frac{1}{x}\right)+C$

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Heather Z.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Catherine R.

Heather Z.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus