Find the integral of 6 7 </mfrac> e <mrow class="MJX-TeXAtom-ORD"> 4

broggesy9

broggesy9

Answered question

2022-05-02

Find the integral of 6 7 e 4 t 6 with respect to t.

Answer & Explanation

alastrimsmnr

alastrimsmnr

Beginner2022-05-03Added 18 answers

Since 6 7 is constant with respect to t, move 6 7 out of the integral.
6 7 e 4 t 6 d t
Let u=4t-6. Then du=4dt, so 1 4 d u = d t. Rewrite using u and du.
6 7 e u 1 4 d u
Combine e u and 1 4
6 7 e u 4 d u
Since 1 4 is constant with respect to u, move 1 4 out the integral.
6 7 ( 1 4 e u d u )
Simplify
3 14 e u d u
The integral of e u with respect to u is e u
3 14 ( e u + C )
Simplify
3 14 e u + C
Replace all occurrences of u with 4t-6
3 14 e 4 t 6 + C

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