Evaluate the indefinite integral as an infinite series.

Evaluate the indefinite integral as an infinite series.
Can someone help me figure this out?

I'm pretty stuck.

Thanks!

arctan(x^5)dx

d/dx [arctan(x)] = 1/(1 + x²)

1/(1 - x) = 1 + x + x² + x³ + ... + xⁿ
1/(1 - (-x)) = 1 - x + x² - x³ + ... + (-x)ⁿ
1/(1 + x²) = 1 - x² + x⁴ - x⁶ + ... + (-x²)ⁿ

Integrate both sides:
arctan(x) = x - x³/3 + x⁵/5 - x⁷/7 + ... + (-1)ⁿ x²ⁿ⁺¹ / (2n+1)

arctan(x⁵) = x⁵ - x¹⁵/3 + x²⁵/5 - x³⁵/7 + ... + (-1)ⁿ x¹⁰ⁿ⁺⁵ / (2n+1)

Write the integral:
∫ arctan(x⁵) dx = ∫ [x⁵ - x¹⁵/3 + x²⁵/5 - x³⁵/7 + ... + (-1)ⁿ x¹⁰ⁿ⁺⁵ / (2n+1)] dx
.................... = ∫ [Σ[n=0,∞] (-1)ⁿ x¹⁰ⁿ⁺⁵ / (2n+1)] dx

http://www.wolframalpha.com/in…
That's the correct series, then you just integrate it. Not sure what you want me to 'recheck', since Wolfram backs me up.

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