How do you integrate by substitution #int x(4x^2+3)^3 dx#?
Scarlett AllisonSee answer below:
By signing up, you agree to our Terms of Service and Privacy Policy
Cameron AlexanderTo integrate by substitution, we set ( u = 4x^2 + 3 ), then differentiate to find ( du = 8x , dx ). Rearrange to solve for ( dx ). The integral becomes ( \frac{1}{8} \int u^3 , du ). Integrate ( u^3 ) to get ( \frac{1}{32}u^4 ), then substitute back for ( u ) to get ( \frac{1}{32}(4x^2 + 3)^4 ). Finally, multiply by ( \frac{1}{8} ) to get the final answer ( \frac{1}{256}(4x^2 + 3)^4 + 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.
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 integrate #int x^2sqrt(16-x^2)# by trigonometric substitution?
- How do you integrate #int (e^x-1)/sqrt(e^(2x) -1)dx# using trigonometric substitution?
- How do you integrate #e^(4x) d#?
- How do you find the antiderivative of #int (x^3cosx) dx#?
- How do you integrate #f(x)=(x^2-2x)/((x^2-3)(x-3)(x-8))# using partial fractions?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7