(1 point) Evaluate the indefinite integral:fk? _ 6)4(2x) dx+C_...

Evaluate the indefinite integral.

$ \displaystyle \int \frac{1 + x}{1 + x^2} \, dx $

In this question We have to integrate the function and that is I can see here X plus one police work. Okay to integrate it let I make a substitution here. I'm going to replace X plus one by you here now we are going to differentiate Okay about tax so we can see that we got here one plus zero as opposed to deal by DX means dX should be close to deal. Okay make these institutions in the integration so you can see that our integration that was of X plus one holy square. The changes into the U. S. Were into bill. Okay because X plus one is replaced by you and the X replaced by. Do you hear now? We are going to apply the power rule that says that access to the power and its integration is given by access to the parent plus one opponent plus one by applying this property with that. Here you're a story about two plus one upon two plus one let's say. And this can be witness you cube by three plus C. Now we have go. They substitute the value of you here. Okay? After the substituting I get here X plus one rest of the power three, divide by three. Let's see. So this is the value of integration that we get here. Okay? Thanks.

Even ghost in his integration off one of on three under X dears, this equals in addition off one of Bonn next to the body off one by three. Dears, this gives us indication off. It's the power off minus one upon three. Dears, this is Eagle Do extent, Barbara to upon three. So do here on DDE. Thio last. See? So this is steady, Bart Hansa to question.

Problem is you violated the integral into girl Kasai Numerous X Jax for this problem where they're used. My third of the integration by parts the formula is into girl. You were prom yaks. It's the culture you have three minus into girl. You prom way, Max. Now, for this problem, we can not you. It's the culture. A sign, humorous X and the light way from thence he goto What then we have you from? Is the cultural negative one over Tough one minus X square on the V is equal to X Now use this formula We have this integral and Nico to call sign inverse tax hams X minus into girl Negative one over beautif one minus X square Ham's x x This is Echo two Ex assign humors EXP lass into girl ax over beautif one minus sacks Claire Jax of this part We can use my third of use of prostitution and the letter U It's the culture one minus x squire, then see you. Is the connective too lax? He hacks so this into girl. It's the culture negative into girl. One half you too negative by half the u. This is Echo two Conectiv, Utah. Well, half this is negative. Beautiful one Manus X squared. Now we know it's anti girl off co sign You were sex yaks. This is the cultural X time school sign and we're sex. And then plus the integral this one that this is minus dilutive one minus six square and it don't forget it asked of cars number C.

We're looking at the integral of Coach engine axe d x We know that cotija axes cosign x o ver sine x, which means now we're looking at the integral of coastline acts over sign acts de axe. Okay. What this means now is that if you is sign acts, then de axe is d'you over co sign X Once we've taken the derivative of science, which is co sacks which means now we know the integral is won over you. Do you which substituting us? Sign X. We end up with our final solution of natural log of sign axe plus C.