Evaluate the integral \int \frac{\log x}{x} \, dx

Evaluate the integral \int \frac{\log x}{x} \, dx

Alex Bettington
Alex Bettington
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Find the points on the cone z^2 = x^2 + y^2 which are closest to the point (1, 2, 0).
Convert the polar equation r = -4csc(theta) into a Cartesian equation.
Find the area of the parallelogram with vertices K(1, 3, 3), L(1, 4, 4), M(4, 8, 4), and N(4, 7, 3).
Given f'(x)=\frac{\cos(x)}{x} and f(4)=3 , find f(x)
Let f(x) = 2x^2 - 2 and let g(x) = 5x + 1. Find the given value. f(g(-1)).
Write the equation 5x + 4y + 7z = 1 in spherical coordinates
Find an equation of the tangent line to the curve y = x^3-3x+1 at the point (1,-1)
Find the radius and interval of convergence of the summation \sum_{n=1}^\infty \frac{ (x+2)^n}{n4^n}
Let f(x) = 7x^2 - 2 to find the following value. f(t + 1).
Find an equation of the plane consisting of all points that are equidistant from (5, 3, -4) and (3, -5, -2), and having -2 as the coefficient of x.
Find the average value of the function h(x) = 6\cos^4 x \sin x on the interval [0, \pi]
Evaluate the integral: integral of 2sec^4 x dx.

Evaluate the integral: integral of 2sec^4 x dx.

Alex Bettington
Alex Bettington
•
Eliminate the parameter t to determine a Cartesian equation for: x = t^2, y = 8 + 4t.
Find an equation for the plane consisting of all points that are equidistant from the points (7, 0, -2) and (9, 12, 0).
Find the slope of the curve: x^3 - 3xy^2 + y^3 = 1 at the point (2, -1).
Find the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(2, 0, 2), Q(-2, 3, 6), R(5, 3, 0), S(-1, 6, 4).
Find all three sides of the triangle with vertices P(2, -1, 0), Q(4, 1, 1), and R(4, -5, 4).
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