Partial integrals have priority over power exponent three, which refer to the integrals of five basic functions: inverse trigonometric function, logarithmic function, power function, exponential function and trigonometric function.

Analysis:

Integral by parts is an important method to calculate integral in calculus. Its main principle is to convert a fraction into another easier integral. That is, no matter how many times the function is exported, it will always appear in the form of the original function.

For example, (x 3/3) e x-(1/3) ∫ x 3d (e x) means (x 3/3) e x.

Application of part-related generalized calculus in integral;

Calculus is developed in application. At first, Newton used calculus and differential equations to deduce Kepler's three laws of planetary motion from the law of universal gravitation. Since then, calculus has greatly promoted the development of mathematics, as well as astronomy, mechanics, physics, chemistry, biology, engineering, economics and other natural sciences, social sciences and applied sciences.

And it is widely used in these disciplines, especially the appearance of computers is more conducive to the continuous development of these applications. Calculus, as a highly interdisciplinary subject, not only has strong practicability in physics and other natural sciences, but also has a strong role in promoting economics.