Use the commutation integral method to find dx x 2 a 2

Let x=atanu, then dx=a(secu) 2 du, dx (x 2+a 2) = secu du

secu(secu+tanu) / (secu+tanu) du

ln|secu+tanu| +c

ln| x+√(x^2+a^2) |c

Because it is in the form of a Riemann Stillges integral, the range of variables in the Riemann Stillgers integral should still be the range of x, not the range of g(x).

Hello teacher, your steps have been changed to this for better understanding.

Let x=atanu, then dx=a(secu) 2 du, dx (x 2+a 2).

asecu╱a du

asecu(secu+tanu)/(asecu+atanu) duln|asecu+atanu| +c

ln| x+√(x^2+a^2) |c

Summary. The commutation method is often used to eliminate the radical in the integrand. When the integrand is a binomial with a high degree, in order to avoid cumbersome formulas, it is sometimes possible to use the second type of commutation method to solve the problem.

There are two commonly used substitution methods: radical substitution and triangular substitution. The first type of commutation integral method = (x-1+1) under the root number (x-1)dx= [under the root number (x-1)+1 under the root number (x-1)]d(x-1)=(2 3)*(x-1) (3 2)+2 under the root number (x-1)+c, where c is an arbitrary constant.

The indefinite integral of 1 (4x -1) is found using the second-type commutation method.

The commutation method is often used to eliminate the radical in the integrand. When the integrand is a binomial with a high degree, in order to avoid cumbersome formulas, it is sometimes possible to use the second type of commutation method to solve the problem. There are two commonly used means of commutation:

Radical substitution, triangular substitution. The first type of commutation integral method = (x-1+1) under the root number (x-1)dx= [under the root number (x-1)+1 under the root number (x-1)]d(x-1)=(2 3)*(x-1) (3 2)+2 under the root number (x-1)+c, where c is an arbitrary constant.

Whether or not I can face my question head-on, the second type of change is to find out.

Original = (x-1+1) Under the root number (x-1)dx= [under the root number(x-1)+1 under the root number(x-1)]d(x-1)=(2 3)*(x-1) (3 2)+2 under the root number(x-1)+c, where c is an arbitrary constant.

Note: This question should be "arctant (1+x 2)dx to find the integral using the commutation method".

Original = arctanxd(arctanx) ydy (order y=arctanx).

y 2 2+c (c is the integration constant).

arctanx)^2/2+c.

The indefinite integral process of finding dx (2sin x+3cos x) by the integral commutation method is as follows:

Commutation integral method is a method of finding integrals. It is derived from the chain rule and the fundamental theorem of calculus.

When calculating the derivative of a function. Composite functions are the most commonly used rule, and to reverse them to find indefinite integrals is to introduce intermediate variables as variable substitutions, and turn one integrative expression into another. In this way, the original product expression is turned into a simpler indefinite integral, which is the commutation integral method.

There are two types of commutation integral methods, the first type of commutation integral method and the second type of commutation integral method.

Go ask your math beast!