Question

F(x)=x-sinxпервообразная ​

Answer 1

Ответ:

cos(x)+((x^2)/2) +C

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Answer 2

To find the antiderivative (indefinite integral) of the function f(x) = x - sin(x), we can apply the integration rules. Let's break it down step by step:

∫ (x - sin(x)) dx

We can integrate each term separately:

∫ x dx - ∫ sin(x) dx

Integrating the first term ∫ x dx is straightforward:

= (1/2)x^2 + C1, where C1 is the constant of integration.

Now, let's focus on integrating the second term ∫ sin(x) dx. The integral of sin(x) is -cos(x):

= -cos(x) + C2, where C2 is the constant of integration.

Combining the results, we have:

∫ (x - sin(x)) dx = (1/2)x^2 - cos(x) + C,

where C = C1 + C2 is the overall constant of integration.