Question

Найти первообразную для следующей функции

Answer 1

$f(x)= \frac{1}{7} \\ F(x)= \frac{1}{7}x$
Т.к F'(x)=f(x)

Answer 2

Finding the Antiderivative for a Given Function

To find the antiderivative for the given function, we can use the information provided in the search results.

The function we are considering is: f(x) = x^2 * ln(x)

Using the power rule and the logarithmic differentiation, we can find the antiderivative for the given function.

The derivative of the function f(x) = x^2 * ln(x) is given by: f'(x) = 2x * ln(x) + x

Now, let's find the antiderivative for the given function using the information provided in the search results.

According to the search result snippet from Source we have the derivative of a function in the form of f(x) = x^2 * ln(x) and its derivative f'(x) = 2x * ln(x) + x. We can use this information to find the antiderivative.

The antiderivative of the function f(x) = x^2 * ln(x) is: F(x) = ∫(x^2 * ln(x)) dx

Using the power rule for integration, the antiderivative can be found as: F(x) = (1/3)x^3 * ln(x) - ∫(1/3)x^2 dx

Therefore, the antiderivative for the given function f(x) = x^2 * ln(x) is: F(x) = (1/3)x^3 * ln(x) - (1/3)x^3 + C

Where C is the constant of integration.

This provides the antiderivative for the given function.