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What is the integral of f divided by the quantity f plus g raised to the power of n with respect to x where f and g are functions of x?
Mrkbh
∫ f(x)/[f(x) + g(x)]n dx = ∫ 1/[f(x) + g(x)]n - 1 dx - ∫ g(x)/[f(x) + g(x)]n dx
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∙ 13y ago
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What is the integral of 1 divided by the quantity 1 plus the square of x with respect to x?
2
What is the integral of 1 divided by the square root of the quantity 1 minus the square of x with respect to x?
0
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 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
What is the integral of 1 divided by the quantity 1 minus the square of x with respect to x?
0
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.
What is the integral of 1 divided by the square root of the quantity 1 plus the square of x with respect to x?
2
What is the integral of 1 divided by the square root of the quantity of the square of x minus 1 with respect to x?
0
What is the integral of the derivative with respect to x of the function f divided by the square root of the quantity f squared plus a constant with respect to x?
∫ f'(x)/√[f(x)2 + a] dx = ln[f(x) + √(f(x)2 + a)] + C C is the constant of integration.
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 quantity f prime times g minus f times g prime divided by the quantity f squared minus 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 = (1/2)ln[(f(x) - g(x))/(f(x) + g(x))] + C
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.
