Calculus Answers

Given that "n" is a positive integer, find
d/dx (x(lnx)^n)

How to find the double point of the curve x^3 + y^3 - 3axy = 0 .?

Integrate x(ln x)^2 dx

using integration by parts to solve
1) ∫ xsin2x dx
2) ∫ xarctanx dx
3) ∫ lnx/(1+x)^2 dx
4) ∫ (lnx)^2 dx

Let u = <5, 6>, v = <-2, -6>. Find -2u + 5v.

Ашnd the volume of the solid of revolution obtained by rotating the curve x=3cos^3(θ) , y=3sin^3(θ) about the x-axis.

how to find the double point of the curve y^2 = (x-2)^2 (x-1) ?

integrate by substitution ∫ (√1+x^2) x^5 dx
integrate by substitution ∫ secx dx, u = secx + tanx

(φ )n = n −1 ∀n∈N , where φ is the Euler-phi function. Is the following statement true? Justify your answer.

Consider the given vector equation.
r(t) = 4eti + 5e−tj
(a) Find r'(t).
r'(t) =


(b) Sketch the plane curve together with the position vector
r(t)
and the tangent vector
r'(t)
for the given value of
t =0