~1 pointsLarCalc11 4.5.503.XP. 0/5 Submissions UsedFind the indefinite integral. (Use C for the constant of integration )Bx7 sin(x8) dxNeed [email protected]

Find the indefinite integrals. $$\int\left(x^{5}-12 x^{3}\right) d x$$

Eso in this problem won't evaluate stroke. It reminds three X tons style five eggs Yes, eso We're going to use integration by parts that you equals to sign off five Thanks. Then the EU will be five times co sign five days TV is equally minus three X gets therefore equals two minus one third its be minus three eggs. So integration by parts we have this integrate cause Tau minus one third Italy minus three eggs sile five bags cross 543 integral off B minus three x Times Co sign five x three x eso for the third this integral. We use integration byproduct game Choose you to be coastal five x. You is minus five. Sign off five eggs TV is Peter T minus three x t x the is minus one third if the minus three x dx So this integral equals thio minus one third Italy. So this is not the X here anymore. Into the minus three x Times Co Sign five x yes minus five Third Integral. It reminds three x Sci five bags The X Come on. There's a combined with this to results. We have the following conclusion. Theologian integral because to minus one third Italy minus three X files five eggs Eso plugging This result into this in Europe, that gives us minus 5/9. Eatery minus three X cause I five x the minus 25/9 Integral. It reminds 38 Sign off. Five x p x. So, from here, we can see that this integral is exactly the Sam is your own Julian to girl. So we can actually solve for this integral by combining these two terms, then divide by the coefficient in front of it. Okay, So our conclusion is this integral. The engine integral the natural because too, so the coefficient equals thio. Now I over 34 times. Um, Italy minus three X comes minus one third sign off five X minus five for one night cause I five x and then we need to mainly at a constant see in the end. So this is the final result? Yes,

In this question we have to find the definite integration in the limits of -5-10. And the function is It is to the power -0.05 XB. It's okay. So let us put that you is -0.05. This shows that Derivatives and deal with. It was to -0.05 bx. No, we can see that dx must be replaced by deal by -0.05 men's minus 20. And we can see here to deal. Okay, so make these replacements. We can say that we have to change the limits also because the whole LTD stands for X variable and we have to find for the knew very well that is you When we put that said it was to -5 Without us. It was 2 -0.05.25. That is zero cool site. And when we put 10 we got minus 0.5 window 10 and that is minus sorry plus- or 0.05-10. That is you can see that minus of five point .50 can say that now the new limits of the integration are minus 0.25 to minus 0.50 And the integration changes into areas to the barrio minus 20. You d oh no minus 20 is a constant. Take it outside integration of areas to the barrio is areas to the barrio. And in this integration we have to substitute the limits. Okay when why I put up our limit I can see that I got here a rest about -0.50 and when I put up a limit always make minus areas to the about minus 0.25 So I can write it that's areas to the power minus one by two- areas to the Power -1 x four. So this is the final simplified answer of this given question here. Okay thank you. Yeah.

Okay we want to integrate the following expression. The integral from 0.5 to one of x squared co tangent of X Q D s. This question is testing our knowledge of methods of integration re previously learned about the power rule, exponential rule and longer rhythmic rules for integration in this section. And for this question particularly we have to use trigonometry and tools so we need to match up which of these. 10 integral corresponds to the form of are given integral. Are integral, history, metric function co tangent. So we see that we're going to be using rule number seven here. That's our solution of the forum. Ln absolute value sign new plus C. Thus we need to identify you to proceed. You is the argument of Catania next cube execute so do you is three X squared dx We're missing a factor of three and are integral, which we carry over to the solution. So our solution is to go from 30.5 to 1 of x squared tangent, X q b x or one third. Ellen sign tube, Synnex cubes from 10.5 to 1 or 2.6365

Hi. So, in this question, we're going to be solving the indefinite integral using the method of you substitution. So we have co sign of five X to the fifth time's the sign of five X D acts of the first thing we're going to do is we're going to set our coasts of five X equal to you. So our d you is going to be equal to the negative. Ah, five sign five x x um, using be a chain role. So from here, we're going to divide both sides by our negative five sign five x and we're going tohave um, that you over negative five Sign of five X is equal to r D X and so we're just going to plug in for our co sign of five x with Are you and r D X with R D You over negative five sign five acts So we're going tohave the integral of you 25 ah times the sign of five x times d you over Negative five sign five x And so from here we can just cross out our signs. Five x Andi, we're going to have the integral of you toothy fifth over negative five d you and we can take out our negative one fit. Some are integral and from here we're just going to be using the equation that states that the integral of X to the N is equal to X to the n plus one over and plus one. So we're going to have negative 1/5 times are you to the five plus 1/5 plus one plus see? And so from here, we're just going to have negative 1/5 times you to the sixth over six plus C. And the last thing we have to do is we have to fill in for our you and are you is equal to the coasts of five X So we're going tohave. Negative one said Times be coasts of five x to the 6/6 plus C, which is equal to the negative coasts. 65 x six of five x, um, over 30 plus C, which is our final answer