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

$\int xar\mathcal{s}c({x}^{2}+1)dx$

Carol Gates
2021-10-17
Answered

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

$\int xar\mathcal{s}c({x}^{2}+1)dx$

You can still ask an expert for help

Neelam Wainwright

Answered 2021-10-18
Author has **102** answers

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

$\int xar\mathcal{s}c({x}^{2}+1)dx$

Solution:

$\int x{\mathrm{sec}}^{-1}({x}^{2}+1)dx$

Let us substitute,

${x}^{2}+1=z$

$2xdx=dz$

Solution:

Now,

$\int \frac{1}{2}{\mathrm{sec}}^{-1}zdz$

$=\frac{1}{2}[{\mathrm{sec}}^{-1}z\int dz-\int [\frac{d}{dz}\left({\mathrm{sec}}^{-1}z\right)\int dz]]$

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

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

Solution:

Let us substitute,

Solution:

Now,

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