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

We now have a known integral.

Hopefully this helps!

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

To find the indefinite integral of ( \int \frac{1}{3x^2 + 3} , dx ), you can use a trigonometric substitution. Let ( u = x\sqrt{3} ). Then ( du = \sqrt{3} , dx ).

After substitution, the integral becomes ( \int \frac{1}{u^2 + 1} , du ), which is a standard integral with respect to ( u ). This integral evaluates to ( \arctan(u) + C ), where ( C ) is the constant of integration.

Substituting back ( u = x\sqrt{3} ), the final result is ( \arctan(x\sqrt{3}) + C ).

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.

- The area under the curve y=e^-x between x=0 and x=1 is rotated about the x axis find the volume?
- How do you find the definite integral of #x/sqrt(2x+1)# from #[0,4]#?
- How do you find the integral of #sin^3(x) cos^5(x) dx#?
- How do you find the antiderivative of #int sinx(cosx)^(3/2) dx#?
- How do you evaluate the integral of #int (1 + cos 4x)^(3/2) dx#?

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