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Fill in the blanks to complete each of the following integration formulas.

tan-1xdx=___

Short Answer

Expert verified

The result isxarctanx-12lnx2+1+C.

Step by step solution

01

Step 1. Given information.

Consider the given integration.

tan-1xdx

02

Step 2. Find the integration.

Apply the by-parts integration method. Consider the values as u=1and v=tan-1x.

tan-1xdx=xtan-1x-x1+x2dx=xtan-1x-x1+x2dxt=1+x2,dt2=xdx=xtan-1x-121tdt=xtan-1x-12lnt+C=xarctanx-12lnx2+1+C

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