Evaluate the indefinite integral.
(Use symbolic notation and fractions where needed. Use $C$ for the arbitrary constant. Absorb into $C$ as much as possible.)
$\int 52 x^{- 1 / 5} \tan (x^{4 / 5}) d x =$

Answer

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Answer

The indefinite integral of $52 x^{- 1 / 5} \tan (x^{4 / 5}) d x$ is $- 65.0 \log (\cos (x^{0.8})) + C$

Steps

Step 1 ：Define the function $f = 52 x^{- 1 / 5} \tan (x^{4 / 5})$

Step 2 ：Calculate the indefinite integral of the function $f$

Step 3 ：The output from the calculation is the integral of the function, which is $- 65.0 \log (\cos (x^{0.8}))$

Step 4 ：However, we need to add the constant of integration, $C$ , to the result

Step 5 ：The indefinite integral of $52 x^{- 1 / 5} \tan (x^{4 / 5}) d x$ is $- 65.0 \log (\cos (x^{0.8})) + C$