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Chapter 5: Q 14. (page 495)

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

鈭�sin-1xdx=_______

Short Answer

Expert verified

The result isxsin-1x+1-x2+C.

Step by step solution

01

Step 1. Given information.

Consider the given integration.

鈭�sin-1xdx

02

Step 2. Find the integration.

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

鈭�sin-1xdx=xsin-1x-鈭�x1-x2dx=xsin-1x-鈭�x1-x2dxt=1-x2,-dt2=xdx=xsin-1x--2鈭�1tdt=xsin-1x--2t2=xsin-1x+1-x2+C

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