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Consider:

we have several approaches for calculating an expression. One of them is T1. Using this approach, we derived some expression for an mathematical problem. For instance, and optimization problem. Now, I want to generate a report that must be submitted to my teacher. It must be formal, articulate, and such that does not strike to a Native as odd!

Compare:

  1. In the case of T1, deriving a closed-form expression for Eq.1 requires solving a complicated integral.

  2. In the case of T1, deriving a closed-form expression for Eq.1 requires a complicated integral to be solved.

  3. In the case of T1, closed-form expression of Eq.1 requires a complicated integral to be solved during the derivation process.

  4. In the case of T1, closed-form expression of Eq.1 requires solving a complicated integral within the derivation process.

The above sentences are all that I can construct with my little knowledge. Can you help me to improve my report. My key purpose is to create a succinct sentence which stands out this point:

solving the complicated Integral is crucial for reaching to the closed-from expression

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  • I come from a math background, and I like number one the best. I can't really justify it though.
    – Em.
    Commented Jun 13, 2016 at 16:36

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Your first sentence sounds great! It is succinct, and uses the simplest verb tenses, which is almost always preferred in writing like this.

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  • Agreed - the meaning of all of them is virtually identical, but #1 phrases things as "X requires Y", which is nice and simple. #2 is almost as good, being "X requires something to be Yed"
    – stangdon
    Commented Jun 13, 2016 at 16:50

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