Primitivas Flashcards
What is the integral of u’ dx?
u
This represents the fundamental theorem of calculus in integral form.
What is the integral of e^u du?
e^u + C
C is the constant of integration.
What is the formula for integration by parts?
∫u’v dx = uv - ∫uv’ dx
This formula helps in integrating products of functions.
What is the integral of sinh u du?
cosh u + C
The hyperbolic sine function integrates to the hyperbolic cosine function.
What is the integral of cosh u du?
sinh u + C
The hyperbolic cosine function integrates to the hyperbolic sine function.
What does the integral of sin u du equal?
-cos u + C
This is the standard integral for the sine function.
What is the integral of cos u du?
sin u + C
The integral of cosine results in sine.
What is the integral of tan u du?
-ln|cos u| + C
The integration of tangent involves the logarithm of the cosine function.
What is the integral of cot u du?
ln|sin u| + C
The integral of cotangent involves the logarithm of the sine function.
What is the integral of arcsin u du?
u arcsin u + √(1 - u²) + C
This is a result from integrating the arcsine function.
What is the integral of arctan u du?
u arctan u - 1/2 ln(1 + u²) + C
This is derived from the integration of the arctangent function.
What is the integral of dx?
x + C
The integral of 1 with respect to x is simply x.
Fill in the blank: The integral of k dx is _______.
kx + C
Here, k is a constant.
True or False: The integral of e^x is e^x + C.
True
This is a fundamental property of exponential functions.
What is the result of integrating the derivative of a function?
The original function plus a constant
This is based on the fundamental theorem of calculus.
