=∫xde^x

=x*e^x-∫e^xdx

=x*e^x-e^x+C

Think about solving problems:

∫ xe xdx = ∫ xd (e x) This is because the differential formula is used: d (e x) = e xdx.

Then ∫ xd (e x) = xe x-∫ e xdx.

This is using the partial integral formula:

∫udv=uv-∫vdu

Finally, xe x-∫ e xdx = xe x-e x+c is obtained.

Finally, there is a constant c because the derivative function is the same, and the original function can differ from any constant c because the derivative of the constant part is 0.

Calculus is a branch of mathematics, which studies the differential and integral of functions and related concepts and applications in higher mathematics. It is the basic subject of mathematics. The content mainly includes limit, differential calculus, integral calculus and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume.

References:

Baidu encyclopedia-calculus