)SAT2400 said:
. tan(4x+1)/4 +c..is the correct answer!An antiderivative is the reverse operation of differentiation. It is a function that, when differentiated, gives the original function back.
An antiderivative is a specific function that satisfies the original function's derivative, while an integral is a general expression that represents the area under the curve of the original function.
The three main methods for finding antiderivatives are the power rule, the substitution method, and integration by parts.
Not all functions have antiderivatives that can be expressed with elementary functions. Some functions, such as ex and sin(x2), have antiderivatives that cannot be expressed in terms of standard mathematical functions.
Antiderivatives are used in science to find the original function from its derivative, which is often important in understanding physical phenomena and making predictions. They are also used in calculus, which is a fundamental tool in many scientific disciplines.