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Single-Step Integration by Parts
Worksheet
Grade Level
Calculus II
CAL2.23 Single-Step Integration by Parts
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For \(\int (x
2
+ 1) \csc
2
{(2 x )}\,dx\), take \(u=x
2
+ 1\) and \(dv=\csc
2
{(2 x )}\,dx\). Which one-step integration-by-parts result is correct? Assume the interval stays in the domain of the functions shown.
A
\(\frac{- x
2
- 1}{2 \tan{(2 x )}} + \int \frac{x}{\tan{(2 x )}}\,dx + C\)
B
\((x
2
+ 1) \csc
2
{(2 x )} - \int 2 x \csc
2
{(2 x )}\,dx + C\)
C
\(\frac{- x
2
- 1}{2 \tan{(2 x )}} - \int \frac{x}{\tan{(2 x )}}\,dx + C\)
D
\(\frac{- x
2
- 1}{2 \tan{(2 x )}} - \int \frac{- x
2
- 1}{2 \tan{(2 x )}}\,dx + C\)
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