# How do you find the indefinite integral of #int 1/(3x+2)#?

See answer below:

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

To find the indefinite integral of (\int \frac{1}{3x+2} , dx), we use the substitution method.

Let (u = 3x + 2), then (du = 3 , dx), or equivalently, (dx = \frac{1}{3} , du).

Substituting these expressions into the integral:

(\int \frac{1}{3x+2} , dx = \int \frac{1}{u} \cdot \frac{1}{3} , du)

Now, we integrate with respect to (u):

(\int \frac{1}{u} \cdot \frac{1}{3} , du = \frac{1}{3} \int \frac{1}{u} , du)

The integral of (\frac{1}{u}) with respect to (u) is (\ln|u| + C), where (C) is the constant of integration.

So, substituting back (u = 3x + 2):

(\frac{1}{3} \int \frac{1}{u} , du = \frac{1}{3} \ln|3x + 2| + C)

Therefore, the indefinite integral of (\int \frac{1}{3x+2} , dx) is (\frac{1}{3} \ln|3x + 2| + C), where (C) is the constant of integration.

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

To find the indefinite integral of ( \int \frac{1}{3x + 2} ):

- Recognize that the given function is in the form ( \frac{1}{ax + b} ), which is a standard form for integration.
- Apply the substitution method: Let ( u = 3x + 2 ). Then, ( du = 3dx ), or ( dx = \frac{1}{3} du ).
- Rewrite the integral in terms of ( u ): ( \int \frac{1}{u} \cdot \frac{1}{3} du ).
- Integrate ( \frac{1}{u} ) with respect to ( u ): ( \frac{1}{3} \ln|u| + C ).
- Substitute back ( u = 3x + 2 ) into the result: ( \frac{1}{3} \ln|3x + 2| + C ).

So, the indefinite integral of ( \frac{1}{3x + 2} ) is ( \frac{1}{3} \ln|3x + 2| + 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 definite integral of #int (2+3x-x^2) dx# from #[1,2]#?
- What is the integral of #int (cosx)/(x) dx#?
- How do you find the indefinite integral of #int (1+secpix)^2secpixtanpixdx#?
- What is the antiderivative of #sqrt(4x² + 1)#?
- How do you evaluate the definite integral #int (x+4)dx# from [-1,3]?

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