Evaluate the Indefinite Integral as a Power Series $\int \tan ^ { - 1 } \left( t ^ { 2 } \right) d t$

question 126

Multiple Choice

Evaluate the indefinite integral as a power series. $\int \tan ^ { - 1 } \left( t ^ { 2 } \right) d t$

• A) \(C + \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } t ^ { 2 n + 3 } } { ( 2 n + 3 ) }\)
• B) \(C + \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } t ^ { 4 n + 3 } } { ( 2 n + 1 ) ( 4 n + 3 ) }\)
• C) \(C + \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } t ^ { 2 n + 2 } } { ( 2 n + 1 ) }\)
• D) \(C + \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } t ^ { 4 n + 2 } } { ( 2 n + 1 ) ( 4 n + 3 ) }\)
• E) \(C + \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } t ^ { 4 n + 3 } } { ( 4 n + 3 ) }\)