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Chapter 5: Q 15. (page 495)

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

鈭�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.

鈭�tan-1xdx

02

Step 2. Find the integration.

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

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

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Most popular questions from this chapter

Describe two ways in which the long-division algorithm for polynomials is similar to the long-division algorithm for integers and then two ways in which the two algorithms are different.

Solve the integral:鈭�lnxdx

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(a) with the trigonometric substitution x = 3 tan u;

(b) with algebra and the derivative of the arctangent.

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