Get the answer to "Evaluate the following integral. ∫sec4(ln⁡0)0d0"

Tolnaio

Answered question

2021-10-17

Evaluate the following integral.

\int \frac{\sec^{4} (\ln 0)}{0} d 0

Jozlyn

Skilled2021-10-18Added 85 answers

Step 1
Given :

\int \frac{\sec^{4} (\ln 0)}{0} d 0

Step 2

\int \frac{\sec^{4} (\ln 0)}{0} d 0

put

u = \ln 0

d u = \frac{1}{0} d 0

= \int \sec^{4} (u) d u

= \int (1 + \tan^{2} (u)) \sec^{2} (u) d u

v = \tan u

d v = \sec^{2} u d u

= \int 1 + v^{2} d v

= \int 1 d v + \int v^{2} d v

= v + \frac{v^{3}}{3} + C

put

v = \tan (\ln 0)

= \tan (\ln (0)) + \frac{\tan^{3} (\ln (0))}{3} + C

\int \frac{\sec^{4} (\ln (0))}{0} d 0 = \tan (\ln (0)) + \frac{\tan^{3} (\ln (0))}{3} + C

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