Explained: "Evaluate the integral. tan⁡h2xdx"

ka1leE

Answered question

2021-10-16

Evaluate the integral.

{\tan h}^{2} x d x

SchepperJ

Skilled2021-10-17Added 96 answers

Step 1
We have to evaluate the integral:

{\tan h}^{2} x d x

We know the identity,

{\tan h}^{2} x + {\sec h}^{2} x = 1

\Rightarrow {\tan h}^{2} x = 1 - {\sec h}^{2} x

Step 2
Rewriting the integral by using identity,

\int {\tan h}^{2} x d x = \int (1 - {\sec h}^{2} x) d x

= \int d x - \int {\sec h}^{2} x d x

= x - \tan h x + C

Where, C is an arbitrary constant.
Hence, value of integration is

x - \tan h x + C

.
Note:
We have used following integration,

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

\int d x = x + C

\int {\sec h}^{2} x d x = \tan h x + C

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