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revistasbibxjm87

revistasbibxjm87

Answered question

2022-05-13

Evaluate 9 7  e tan ( 5 x ) sec 2 ( 5 x ) d x.

Answer & Explanation

Bumanro5mv

Bumanro5mv

Beginner2022-05-14Added 9 answers

Simplify.

9etan(5x)sec2(5x)7dx

Since 97 is constant with respect to x, move 97 out of the integral.

97etan(5x)sec2(5x)dx

Let u2=tan(5x). Then du2=5sec2(5x)dx, so 15du2=sec2(5x)dx. Rewrite using u2 and du2.

97eu215du2

Combine eu2 and 15.

97eu25du2

Since 15 is constant with respect to u2, move 15 out of the integral.

97(15eu2du2)

Simplify.

935eu2du2

The integral of eu2 with respect to u2 is eu2.

935(eu2+C)

Simplify.

935eu2+C

Replace all occurrences of u2 with tan(5x).

935etan(5x)+C

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