FIND EACH INDEFINITE INTERGRAL
(X^2+1)^9 2X DX
To find the indefinite integral of the expression (x^2 + 1)^9 * 2x dx, we can use the method of substitution.
Let's start by setting u = x^2 + 1. Taking the derivative of both sides with respect to x, we get du/dx = 2x. Solving for dx, we can rewrite our expression as (u^9)*(du).
Now, our task is to find the indefinite integral of u^9 du.
Using the power rule for integration, we increase the exponent by 1 and divide by the new exponent. In this case, we increase the exponent 9 by 1 to get 10, and divide by 10 to get (1/10). Therefore, the indefinite integral of u^9 du is (1/10) * u^10 + C, where C is the constant of integration.
Finally, substituting back u = x^2 + 1, we get the indefinite integral of (x^2 + 1)^9 * 2x dx to be:
(1/10) * (x^2 + 1)^10 + C
So, the result of finding the indefinite integral is (x^2 + 1)^10/10 + C, where C is the constant of integration.