We can solve the integral by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it ), which when substituted makes the integral easier. We see that it's a good candidate for substitution. Let's define a variable and assign it to the choosen part
Now, in order to rewrite in terms of , we need to find the derivative of . We need to calculate , we can do that by finding the derivative of the equation above
Isolate in the previous equation
Substituting and in the integral and simplify
We can solve the integral by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it ), which when substituted makes the integral easier. We see that it's a good candidate for substitution. Let's define a variable and assign it to the choosen part
Now, in order to rewrite in terms of , we need to find the derivative of . We need to calculate , we can do that by finding the derivative of the equation above
Isolate in the previous equation
Substituting and in the integral and simplify
The integral of the inverse of the lineal function is given by the following formula,
Replace with the value that we assigned to it in the beginning:
Replace with the value that we assigned to it in the beginning:
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration
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