Evaluate the indefinite integral

3 Answers

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(Let y = integral x to the power of 2 italic tan to the power of minus 1 end exponent open parentheses 2 x close parentheses d x )

$space space space space space space space space space space space space space space space space space y equal x to the power of 2 over 5 open square brackets open parentheses 2 x italic tan to the power of minus 1 end exponent open parentheses 2 x close parentheses close parentheses minus 1 over 2 italic log open vertical bar 1 plus 4 x to the power of 2 close vertical bar plus C close square brackets plus 1 over 5 open square brackets integral open square brackets x italic log open vertical bar 1 plus 4 x to the power of 2 close vertical bar close square brackets d x close square brackets plus fraction numerator C x over denominator 5 end fraction$ .