Which Integral Form Matches the Simplification of x(lnx)^2 dx?

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In summary, simplification in calculus involves reducing complex mathematical expressions to their simplest form using techniques such as factoring, combining like terms, and canceling out common factors. It is important because it helps us better understand and analyze complex concepts. Common techniques used for simplification include factoring, expanding, combining like terms, using the distributive property, and canceling out common factors. To improve skills in simplification, regular practice and review of basic algebraic concepts is recommended. However, it is important to avoid potential pitfalls such as forgetting to apply algebraic rules, making calculation errors, and overlooking important constants or variables. Double-checking work and being mindful of potential errors can help avoid these pitfalls.
  • #1
electronicxco
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I have found for the integral of x(lnx)^2 dx to be :
((1)/(4)x^2)(2(ln(x)-1)ln(x)+1)

but i need it to be in one of these forms:
these are the choices:
x^2((lnx)^2 + lnx- (1/2)) +C
1/2 x^2 ((lnx)^2 +lnx + 1/2) +C
x^2((lnx)^2 + lnx + (1/2)) + C
x^2((lnx)^2 - lnx + (1/2)) + C
1/2 x^2 ((lnx)^2 -lnx + 1/2) +C
1/2 x^2 ((lnx)^2 -lnx - 1/2) +C

Thanks!
 
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  • #2
((1)/(4)x^2)(2(ln(x)-1)ln(x)+1) = (1/2)x^2[(ln(x) - 1)ln(x) + 1/2] = 1/2 x^2 ((lnx)^2 -lnx + 1/2), so

1/2 x^2 ((lnx)^2 -lnx + 1/2) +C

is the correct choice.
 

FAQ: Which Integral Form Matches the Simplification of x(lnx)^2 dx?

What is simplification in calculus?

Simplification in calculus refers to the process of reducing complex mathematical expressions or equations to their simplest form. This involves using various algebraic techniques, such as factoring, combining like terms, and canceling out common factors.

Why is simplification important in calculus?

Simplification is important in calculus because it allows us to better understand and analyze complex mathematical concepts. By simplifying equations, we can identify key patterns and relationships, which can help us solve problems and make predictions.

What are some common techniques used for simplification in calculus?

Some common techniques used for simplification in calculus include factoring, expanding, combining like terms, using the distributive property, and canceling out common factors. Additionally, the use of trigonometric identities and logarithmic rules can also aid in simplification.

How can I improve my skills in simplification for calculus?

To improve your skills in simplification for calculus, it is important to practice regularly and review basic algebraic concepts. You can also seek out additional resources, such as textbooks or online tutorials, to reinforce your understanding of simplification techniques.

Are there any potential pitfalls to avoid when simplifying in calculus?

Yes, there are a few potential pitfalls to be aware of when simplifying in calculus. These include forgetting to apply certain algebraic rules, making mistakes in calculations, and overlooking important constants or variables. It is important to double-check your work and be mindful of any potential errors.

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