Solv Indefinite Integral: x^3/sqrt[1 + x^2] dx

In summary, a solv indefinite integral is a calculus operation that finds the function whose derivative is equal to the given function. To solve the indefinite integral of x^3/sqrt[1 + x^2], the substitution method can be used. The sqrt[1 + x^2] in the denominator is a result of this method, and solving indefinite integrals can have various applications in fields like physics and engineering. There is no single formula for solving indefinite integrals, but different techniques can be used depending on the function being integrated.
  • #1
JimmyCat
1
0
I'm having a problem with the following integral: x^3/sqrt[1 + x^2] dx

Can this be done with substitution or integration by parts?
Throw me some hints at this one please!

Sorry I forgot to include my attempt.

I tried solving this by substitution, letting u=1-x^2. Then letting (-1/2)du = xdx. Simplifying it down and came to the answer of 1/3(1-x^2)-sqrt(1-x^2) + C
 
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  • #2
Please make an attempt at the solution, or this thread will be deleted.
 

What is a solv indefinite integral?

A solv indefinite integral is an operation in calculus that finds the function whose derivative is equal to the given function. It is essentially the reverse operation of taking a derivative.

How do I solve the indefinite integral of x^3/sqrt[1 + x^2]?

To solve this indefinite integral, you can use the substitution method. Let u = 1 + x^2, then du = 2x dx. This allows you to rewrite the integral as ∫ (x^2/sqrt[u]) du. From here, you can use the power rule for integration and then substitute back in for u to find the final answer.

Why is there a sqrt[1 + x^2] in the denominator?

The sqrt[1 + x^2] in the denominator is a result of the substitution method used to solve the indefinite integral. It allows for the integral to be rewritten in a form that can be more easily integrated using the power rule.

What are the possible applications of solving indefinite integrals?

Solving indefinite integrals can be used in various fields, such as physics, engineering, and economics. It can help in finding the displacement, velocity, or acceleration of an object, determining the area under a curve, and solving optimization problems, among other applications.

Is there a general formula for solving indefinite integrals?

There is no single formula for solving indefinite integrals, as it depends on the specific function being integrated. However, there are various integration techniques, such as substitution, integration by parts, and trigonometric substitution, that can be used to solve different types of indefinite integrals.

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