How do you find the antiderivative of #int (x^3cosx) dx#?
Now, plugging this into the IBP formula:
Thus:
Pay close attention to sign:
IBP again on the integral:
So:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the antiderivative of ( \int x^3 \cos(x) , dx ), you can use integration by parts. Let ( u = x^3 ) and ( dv = \cos(x) , dx ). Then, ( du = 3x^2 , dx ) and ( v = \sin(x) ). Apply the integration by parts formula:
[ \int u , dv = uv - \int v , du ]
Substitute the values:
[ \int x^3 \cos(x) , dx = x^3 \sin(x) - \int \sin(x) \cdot 3x^2 , dx ]
Integrate ( \int \sin(x) \cdot 3x^2 , dx ) using integration by parts again or by using a simple substitution. Then, simplify the expression if necessary.
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+1)/((x-9)(x+8)(x-2))# using partial fractions?
- How do you find the integral of #tanˉ¹(2x) dx#?
- How do you integrate #int(6x^2+7x-6)/((x^2-4)(x+2))dx# using partial fractions?
- How do you integrate #int (2x+1)/((x-4)(x-1)(x+7)) # using partial fractions?
- How do you evaluate the integral #int (x-2)/(3x(x+4))#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7