Integral of 1 (x^2 + 2) dx - 2) dx ? • Physics Forums Also the integral of 1 x^2+1 is a standard integral, evaluating to arctan (x) + C I know you can make it look like with a trivial substitution which was already given in this thread but the question is then is there a clever trick that makes it much easier to integrate than using other substitutions after that?
What is the Integral of -e^ (-x)? - Physics Forums A later reply discusses the integral of 2x e^ (x^2) and questions whether the integral of f' (x)e^f (x) is always e^f (x), regardless of the nature of f' (x) Participants express that one cannot derive integrals without prior knowledge of their results, highlighting the challenge of integration
Prove that the integral is equal to ##\pi^2 8## • Physics Forums Prove ∫ 0 2 4 1 x x 2 arcsin (x 1) (x 1 + x 9 16 x) 1 2 x d x = π 2 8 Let The representation integral of is Plugging identity above into with , we obtain Since the integrand is non-negative and continuous over the rectangular domain ( is the root of the numerator), Fubini's Theorem allows us to interchange the order: where and are the closed solutions of the equation Now, computing the
Why integrating sin^2(wt) gives the half-period? - Physics Forums Do you know what the integral of \sin^2x is? If you don't, use the cosine double angle formula \cos 2x = \cos^2x - \sin^2x and the Pythagorean identity \sin^2x + \cos^2x = 1 to express \sin^2x in terms of \cos 2x
Integration of x^2 (xsinx+cosx)^2 - Physics Forums Hi everyone, First of all, this isn't really a "homework", I've completed my calculus course and I'm just curious about this problem Homework Statement \\int\\frac{x^{2}}{(xsinx+cosx)^{2}} dx Homework Equations Trigonometric substitutions, integration by parts maybe? The
How Do You Integrate (dx dt) dx in Physics Problems? Participants explore different approaches to rewriting the integral and the implications of variable dependencies One participant asks how to integrate ∫ b (dx dt) ⋅ dx, mentioning difficulty in substituting dx with v dt