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What is the integral of the quantity of the derivative with respect to x of the function f times another function of x defined as g subtracted by g prime times f divided by g squared with respect to x?
∫ [f'(x)g(x) - g'(x)f(x)]/g(x)2 dx = f(x)/g(x) + C C is the constant of integration.
What is the integral of -2x divided by the square root of x squared minus 4?
- ln ((x^2)-4)
What is the integral of 1 divided by x to the power of 0.999?
1.001
What is the integral of the quantity f prime times g minus f times g prime divided by the quantity f squared plus g squared with respect to x where f and g are functions of x?
∫ [f'(x)g(x) - f(x)g'(x)]/(f(x)2 + g(x)2) dx = arctan(f(x)/g(x)) + C C is the constant of integration.
Integral of 1 divided by x cubed?
I will assume that this is sopposed to be integrated with respect to x. To make this problem easier, imagine that the integrand is x raised to the negative 3. The integral is 1/(-2x-2) plus some constant c.
What is the integral of the derivative with respect to x of f divided by the quantity p squared plus q squared f squared with respect to x where f is a function of x and p and q are constants?
∫ f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)
What is the integral of the derivative with respect to x of f divided by the quantity q squared f squared minus p squared with respect to x where f is a function of x and p and q are constants?
∫ f'(x)/( q2f(x)2 - p2) dx = [1/(2pq)ln[(qf(x) - p)/(qf(x) + p)]
What is the integral of f prime divided by the quantity a times the square of f plus b times f with respect to x where f is a function of x and a and b are constants?
∫ f'(x)/(af(x)2 + bf) dx = (1/b)ln[f(x)/(af(x) + b)] + C C is the constant of integration.
What is the integral of f divided by the quantity 1 minus f with respect to x where f is a function of x?
∫ f(x)/(1 - f(x)) dx = -x + ∫ 1/(1 - f(x)) dx
How do you integrate the integral of quantity of x plus 2 divided by x squared plus x plus 1?
3
Equation for marginal cost and average cost?
Marginal cost - the derivative of the cost function with respect to quantity. Average cost - the cost function divided by quantity (q).
What is the integral of 1 divided by the quantity of a function of x multiplied by the quantity of that same function plus or minus another function of x with respect to x?
∫ [1/[f(x)(f(x) ± g(x))]] dx = ±∫1/[f(x)g(x)] dx ± (-1)∫ [1/[g(x)(f(x) ± g(x))]] dx
What is the integral of f prime divided by the quantity f times the square root of the quantity f squared minus a squared with respect to x where f is a function of x and a is a constant?
∫ f'(x)/[f(x)√(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C C is the constant of integration.
What is the integral of the derivative with respect to x of the function f divided by the square root of the quantity a times f plus b with respect to x?
∫ f'(x)/√(af(x) + b) dx = 2√(af(x) + b)/a + C C is the constant of integration.
What is the integral of 2 times x divided by the quantity x plus 1 to the third power?
3
What is the integral of f prime divided by the square root of the quantity a squared minus f squared with respect to x where f is a function of x and a is a constant?
∫ f'(x)/√(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.
What is the integral of 1 divided by the quantity 1 plus the square of x with respect to x?
2
