# How do you evaluate the integral #int (x-1)/(x+1)dx#?

Split the integrand function:

Using the linearity of the integral:

These are standard integrals that we can solve directly:

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the integral (\int \frac{x - 1}{x + 1} , dx), you can use substitution method.

Let (u = x + 1), then (du = dx).

Substitute: [ \int \frac{x - 1}{x + 1} , dx = \int \frac{u - 2}{u} , du ]

Now, divide: [ \int \frac{u - 2}{u} , du = \int \left(1 - \frac{2}{u}\right) , du ]

Integrate: [ \int \left(1 - \frac{2}{u}\right) , du = \int 1 , du - \int \frac{2}{u} , du ]

[ = u - 2 \ln|u| + C ]

Substitute back: [ = (x + 1) - 2 \ln|x + 1| + C ]

Where (C) is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the integral of #int (dx / x^(2/3)) # from 1 to -15?
- What is the Integral of #tan^2(x)sec(x)#?
- How do you find the sum of the finite geometric sequence of #Sigma 2(-1/4)^n# from n=0 to 40?
- How do you evaluate the integral #int1/(1+x^2)^2 dx# from #-oo# to #oo#?
- How do you find the antiderivative of #f(x)=(2x^2-5x-3)/(x-3)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7