Math  /  Calculus

Question2. [-/3 Points] DETAILS MY NOTES SCALCET9 11.10.062.
Evaluate the indefinite integral as an infinite series. arctan(x6)dxn=0()+c\begin{array}{r} \int \arctan \left(x^{6}\right) d x \\ \sum_{n=0}^{\infty}(\square)+c \end{array} Need Help? Readif Submit Answer

Studdy Solution
Write the result as an infinite series plus the constant of integration CC:
arctan(x6)dx=n=0(1)nx12n+7(2n+1)(12n+7)+C\int \arctan(x^6) \, dx = \sum_{n=0}^{\infty} \frac{(-1)^n x^{12n+7}}{(2n+1)(12n+7)} + C
The indefinite integral evaluated as an infinite series is:
n=0(1)nx12n+7(2n+1)(12n+7)+C\sum_{n=0}^{\infty} \frac{(-1)^n x^{12n+7}}{(2n+1)(12n+7)} + C

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