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Determine the Integral by Making an Appropriate Substitution ∫sec⁡2x(1−3tan⁡x)1/2\int \frac { \sec ^ { 2 } x } { ( 1 - 3 \tan x ) ^ { 1 / 2 } }

Question 70

Multiple Choice

Determine the integral by making an appropriate substitution.
- ∫sec⁡2x(1−3tan⁡x) 1/2\int \frac { \sec ^ { 2 } x } { ( 1 - 3 \tan x ) ^ { 1 / 2 } } dx


A) ln ∣1−3tan⁡x∣| 1 - 3 \tan x | + C
B) - 23\frac { 2 } { 3 } ln ∣1−3tan⁡x∣| 1 - 3 \tan x | + C
C) - 23\frac { 2 } { 3 } (1−3tan⁡x) 1/2( 1 - 3 \tan x ) ^ { 1 / 2 } + C
D) (1−3tan⁡x) 1/2( 1 - 3 \tan x ) ^ { 1 / 2 } + C
E) none of these

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