Solved: "Solve the integral. ∫3sec⁡(2x−1)tan⁡(2x−1)dx"

gamomaniea1

Answered question

2021-11-09

Solve the integral.

\int 3 \sec (2 x - 1) \tan (2 x - 1) d x

Stephanie Mann

Beginner2021-11-10Added 25 answers

Step 1
Given integral is

\int 3 \sec (2 x - 1) \tan (2 x - 1) d x

We will use the following substitution to evaluate the integral.
2x-1=t
2dx=dt

d x = \frac{1}{2} d t

Step 2
Therefore, we have

\int 3 \sec (2 x - 1) \tan (2 x - 1) d x = \frac{3}{2} \int \sec t \tan t d t

We know that integral of secxtanxdx is secx+c
Therefore,

\int 3 \sec (2 x - 1) \tan (2 x - 1) d x = \frac{3}{2} \sec t + c

\int 3 \sec (2 x - 1) \tan (2 x - 1) d x = \frac{3}{2} \sec (2 x - 1) + c

Step 3
Ans:

\int 3 \sec (2 x - 1) \tan (2 x - 1) d x = \frac{3}{2} \sec (2 x - 1) + c

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