What is &#x222B;<!-- ∫ --> 7 8 </mfrac> <mrow class="MJX-TeXAtom-ORD"> &#xFEFF

airesex2

airesex2

Answered question

2022-04-30

What is 7 8  e 2 t 1 d t?

Answer & Explanation

drenkttj9

drenkttj9

Beginner2022-05-01Added 20 answers

Let u=2t-1. Then du=2dt, so 1 2 d u = d t. Rewrite using u and du.
7 8 e u 1 2 d u
Simplify.
7 e u 16 d u
Since 7 16 is constant with respect to u, move 7 16 out of the integral.
7 16 e u d u
The integral of e u with respect to u is e u
7 16 ( e u + C )
Simplify.
7 16 e u + C
Replace all occurrences of u with 2t-1.
7 16 e 2 t 1 + C

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