Recent content by NotaMathPerson

I am planning to read and study a book in math. How do you guys take notes when reading Mathematics books? I don't go to class anymore. I plan to self-study it. Any tips would be helpful! Thanks.

How did you do that expanded form?

$$\int(1-y^2)^\frac{1}{2}\,dy$$ I did trig substitution $$y=\sin\theta$$ $$dy=\cos\theta\,d\theta$$ $$\int(1+\cos2\theta)d\theta$$ $$\arcsin\,y+\frac{1}{2}\sin(2\arcsin\,y)+c$$ How do I get rid of the arcsins?

Please check my solution. $$-\frac{1}{\sqrt{2}}\int\frac{u^2}{1-u^2}\,du$$Using partial fraction decomposition $$\frac{u^2}{1-u^2}=\frac{u^2}{(1-u)(1+u)}=\frac{A}{1-u}+\frac{B}{1+u}$$ u=1; A = 0.5 u=-1; B =0.5 $$\frac{0.5}{1-u}+\frac{0.5}{1+u}$$...

Yes i did that already. What I am after is the answer as to why the method i used above did not work.

Do you mean $$u=2x^2-1$$ $$du=4xdx$$ there's still an x.

Solve the ode $$(y-2x^2y)dx +xdy = 0$$ The equation is in exact form $$Q(x,y)dx+ P(x,y)dy =0$$ When I test for exactness it fails. Then I used the technique $$\frac{M_y-N_x}{N}$$ I get $u(x)=-2x$ as my integrating factor. But I end still end up with a non-exact d.e why is that...

I need some help with this integran $$\int\frac{2x^2}{2x^2-1}dx$$I can't seem to solve this using the techniques that I know. What method should I use?

Can we integrate it using partial fractions?

$$\int\frac{\sec^2\theta\,d\theta}{(\tan\theta)(1+\tan^2\theta)}$$ $$\int\frac{\sec^2\theta\,d\theta}{(\tan\theta)(\sec^2\theta)}$$ $$\int\frac{d\theta}{\tan\theta} = \int\frac{\cos\theta\,d\theta}{\sin\theta}$$ Using u substitution $$\ln|\sin\theta| +c$$ since $$x = \tan\theta =...

I used substitution but did not get a form I know how to integrate. What technique should I use here? $\int\frac{1}{x(x^2+1)}dx$ Thanks!

Re: Trigonometric equatio Hello soroban! How did you get the value for x?

A=3sinx+4cosx and B=3cosx-4sinx if B = 4 find A. What i tried is to use 4=3cosx-4sinx and solve for cosx now cosx = (4+4sinx)/3 plug this into A I end up getting A = (25sinx+16)/3 am I correct?

Oh yes. I forgot. It should be -44/125

Hello! I get cos(A-B)=(3/5)(24/25)+(4/5)(7/25)= 0.8 is thus correct?