Answered: "Evaluate the following integral. ∫xsec⁡h2xdx"

Rui Baldwin

Answered question

2021-10-30

Evaluate the following integral.

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

Nathanael Webber

Skilled2021-10-31Added 117 answers

Step 1
To evaluate the integral:

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

Solution:
Integral by parts states that:

\int u d v = u v - \int v d u

Evaluating the integral by parts.

\int x {\sec h}^{2} x d x = x \int {\sec h}^{2} x d x - \int [\frac{d}{d x} (x) \int {\sec h}^{2} x d x] d x

= x \tan h (x) - \int \tan h (x) d x

= x \tan h (x) - \ln (\cos h (x)) + C

Step 2
Hence, required answer is

x \tan h (x) - \ln (\cos h (x)) + C

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