# How do you integrate #int x^2 csc x dx # using integration by parts?

You will need some more advanced mathematics than just integration by parts.

WolframAlpha gives an answer involving complex values functions including the complex valued polylogarithm function.

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

To integrate ∫x^2 csc(x) dx using integration by parts, we choose ( u = x^2 ) and ( dv = csc(x) dx ). Then, we find ( du ) and ( v ) as follows:

( du = 2x dx )

( v = -ln|csc(x) + cot(x)| )

Applying the integration by parts formula:

[ \int u dv = uv - \int v du ]

we get:

[ \int x^2 csc(x) dx = -x^2 ln|csc(x) + cot(x)| - \int (-ln|csc(x) + cot(x)|)2x dx ]

Simplify and integrate the remaining term if possible.

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 use partial fractions to find the integral #int (x^2+x+3)/(x^4+6x^2+9)dx#?
- How do you use substitution to integrate #(x^2)(sinx^3) #?
- What is #f(x) = int (x-3)^2-3x+4 dx# if #f(2) = 4 #?
- Is it possible to solve this integrate by integrate substitution method?
- What is #f(x) = int 2sin4x+tanx dx# if #f(pi/4)=1 #?

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