Integral Calculus Answers

find the integral of ∫(((2x+7)))/(x^3-3x^2+2x)

Find the integral of ∫(y-5) dy ∕ y^2 + 5y + 6

Determine whether there is a function phi such that F = grad(phi), where:
a) F = (xz-y)i + (x^2y+z^3)j + (3xz2-xy)k.
b) F = 2xe^(-y)i + (cosz - x^2e^(-y))j - (ysinz)k. If so, find it.

Verify Green's Theorem in the plane for integral_c [(x^2-xy^3)dx +(y^2-2xy)dy] where C is a square with vertices at (0,0), (2,0), (2,2), (0,2).

prove that integral of sin^2wdw/w^2 having limits 0 to infinite =pi/2 ??

(tan2x+cot2x)^2dx

(sin[x])(cos[x/2])
e^arctan[x]/1+x^2

Use a definite integral to find the area under the curve between the given x-values.
f(x) = x−1 + x5 from x = 1 to x = 2

am stuck with this question:

f belongs to L1(0,infinity)

want to prove lim_t->infinity 1/t^2* interal{0 to t }x^2 *f(x)dx=0

∫∫∫2y2z dxdzdy ?
∫∫∫dzdxdy ?