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Q: 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?

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A polynomial function is simply a function that is made of one or more mononomials. For example 4x^2+3x-5 A rational function is when a polynomial function is divided by another polynomial function.

Tangent (theta) is defined as sine (theta) divided by cosine (theta). In a right triangle, it is also defined as opposite (Y) divided by adjacent (X).

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Perhaps you are referring to the trigonometric function sin which is defined as the opposite divided by the hypotenuse. if you then the opposite is refereeing to the side that is opposite the angle, or the side that is furthest away from the angle.

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âˆ« f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)

âˆ« f'(x)/( q2f(x)2 - p2) dx = [1/(2pq)ln[(qf(x) - p)/(qf(x) + p)]

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âˆ« f(x)/(1 - f(x)) dx = -x + âˆ« 1/(1 - f(x)) dx

âˆ« [1/[f(x)(f(x) Â± g(x))]] dx = Â±âˆ«1/[f(x)g(x)] dx Â± (-1)âˆ« [1/[g(x)(f(x) Â± g(x))]] dx

âˆ« f(x)/[(f(x) + b)(f(x) + c)] dx = [b/(b - c)] âˆ« 1/(f(x) + b) dx - [c/(b - c)] âˆ« 1/(f(x) + c) dx b â‰ c

âˆ« f'(x)/[f(x)âˆš(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C C is the constant of integration.

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âˆ« f'(x)/âˆš(af(x) + b) dx = 2âˆš(af(x) + b)/a + C C is the constant of integration.

The quantity that is divided by the surface area is force. Force divided by surface area is equal to pressure.

âˆ« f'(x)/âˆš(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.

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