`int (t^2 - cos(t)) dt` Find the indefinite integral.

Textbook Question

Chapter 4, 4.1 - Problem 26 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the indefinite integral, hence, you need to split the integral, such that:

`int (t^2 - cos t) dt = int t^2 dt - int cos t dt`

You need to use the following formula `int t^n dt = (t^(n+1))/(n+1) + c`

`int t^2 dt = (t^3)/3+ c `

`int cos t dt = sin t + c`

Gathering the results yields:

`int (t^2 - cos t) dt = (t^3)/3 - sin t + c`

Hence, evaluating the indefinite integral, yields` int (t^2 - cos t) dt = (t^3)/3 - sin t + c.`

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