Best solutions to - "Solve the integral. ∫sec⁡hxtan⁡hx0+sec⁡h2xdx"

Tabansi

Answered question

2021-10-22

Solve the integral.

\int \frac{\sec h x \tan h x}{0 + {\sec h}^{2} x} d x

wornoutwomanC

Skilled2021-10-23Added 81 answers

Step 1
Given integral is

I = \int \frac{\sec h x \tan h x}{0 + {\sec h}^{2} x} d x

Substitute

\sec h x = t

\sec h x \tan h x d x = - d t

Integral would be

I = - \int \frac{1}{3^{2} + t^{2}} d t

Step 2
It is known that

\int \frac{1}{a^{2} + x^{2}} d x = \frac{1}{a} \tan^{- 1} (\frac{x}{a}) + C

Thus,

I = - \frac{1}{3} \tan^{- 1} (\frac{x}{a}) + C

Thus,

I = - \frac{1}{3} \tan^{- 1} (\frac{t}{3}) + C

Put

\sec h x = t

we get

I = - \frac{1}{3} \tan^{- 1} (\frac{\sec h x}{3}) + C

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