Solved: "In the given equation as follows , use..."

Carol Gates

Answered question

2021-10-17

In the given equation as follows , use a table of integrals to find the indefinite integral:

\int x a r s c (x^{2} + 1) d x

Neelam Wainwright

Skilled2021-10-18Added 102 answers

In the given equation as follows , use a table of integrals to find the indefinite integral:-

\int x a r s c (x^{2} + 1) d x

Solution:

\int x \sec^{- 1} (x^{2} + 1) d x

Let us substitute,

x^{2} + 1 = z

2 x d x = d z

Solution:
Now,

\int \frac{1}{2} \sec^{- 1} z d z

= \frac{1}{2} [\sec^{- 1} z \int d z - \int [\frac{d}{d z} (\sec^{- 1} z) \int d z]]

= \frac{1}{2} [z \sec^{- 1} z - \frac{1}{\sqrt{z^{2} - 1}} z]

= \frac{1}{2} [(x^{2} + 1) \sec^{- 1} (x^{2} + 1) - \frac{x^{2} + 1}{\sqrt{{(x^{2} + 1)}^{2} - 1}}] + C

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