Calculus. Taking the anti-derivative / integration?

Question

Given that velocity = v(t) = tlnt - t , find the expression (or anti-derivative) for the position x(t).

I don't know how to take the anti-derivative of the tlnt part =\

Answer 1

you can use integration by parts to solve tln(t) part:

let u=ln(t), du=1/t dt
let dv=tdt, v= (t^2)/2

Then, the integral of tln(t) becomes uv-integral of (vdu), which is:
ln(t)*(t^2)/2-integral of [(t^2)/2*(1/t)]dt
=ln(t)*(t^2)/2- integral of (t/2) dt

It is trusted that you can solve the question after this step.

Answer 2

those are very perplexing anti-derivatives. Are you confident you do not opt for to discover the derivatives? Are you in a great-better classification? Your wording seems such as you're a beginning up calculus student, however the matters are hyper perplexing. I taught calculus for some years. ------------------- (a million) we could desire to enable u=x^5+x^4+a million then the subject will become locate the critical of u^2/x*du yet that's not actual calculated. My wager is you may could multiply the expression out to 27 monomials and do each and every.

Answer 3

Taking The Antiderivative