0
What is the integral of a constant multiplied by a function of x with respect to x?
Mrkbh
∫ af(x) dx = a ∫ f(x) dx
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
What is the integral of the derivative with respect to x of a function of x divided by that same function of x with respect to x?
∫ f'(x)/f(x) dx = ln(f(x)) + C C is the constant of integration.
What is the integral of a constant to the power of x with respect to x?
∫ ax dx = ax/ln(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 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 derivative with respect to x of the integral of a function of x with respect to x?
d/dx ∫ f(x) dx = f(x)
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 a function of x raised to the power of n multiplied by the derivative with respect to x of that same function of x with respect to x?
∫ f(x)nf'(x) dx = f(x)n + 1/(n + 1) + C n ≠-1 C is the constant of integration.
What is the integral of the derivative with respect to x of a function of x with respect to x?
∫ d/dx f(x) dx = f(x) + C C is the constant of integration.
What is the integral of the derivative with respect to x of a function of x divided by that same function of x with respect to x?
∫ f'(x)/f(x) dx = ln(f(x)) + C C is the constant of integration.
What is the integral of the derivative with respect to x of the function f multiplied by the quantity a times f plus b raised to the power of n with respect to x?
∫ f'(x)(af(x) + b)n dx = (af(x) + b)n + 1/[a(n + 1)] + C C is the constant of integration.
What is the integral of the derivative with respect to x of a function of x multiplied by another function of x with respect to x?
∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g/(x) dx This is known as integration by parts.
What is the integral of a constant to the power of x with respect to x?
∫ ax dx = ax/ln(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 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 e to the power of x with respect to x?
∫ ex dx = ex + CC is the constant of integration.
What is the derivative with respect to x of the integral of a function of x with respect to x?
d/dx ∫ f(x) dx = f(x)
What is the integral of the sine of x with respect to x?
∫ sin(x) dx = -cos(x) + CC is the constant of integration.
What is the integral of the cosine of x with respect to x?
∫ cos(x) dx = sin(x) + CC 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.
