Determine the integral by making an appropriate substitution.
-$\int \frac { \sec ^ { 2 } x } { ( 1 - 3 \tan x ) ^ { 1 / 2 } }$ dx
A) ln $| 1 - 3 \tan x |$ + C
B) - $\frac { 2 } { 3 }$ ln $| 1 - 3 \tan x |$ + C
C) - $\frac { 2 } { 3 }$ $( 1 - 3 \tan x ) ^ { 1 / 2 }$ + C
D) $( 1 - 3 \tan x ) ^ { 1 / 2 }$ + C
E) none of these

Question

Determine the integral by making an appropriate substitution. 
-$\int \frac { \sec ^ { 2 } x } { ( 1 - 3 \tan x ) ^ { 1 / 2 } }$ dx
A) ln $| 1 - 3 \tan x |$ + C
B) - $\frac { 2 } { 3 }$ ln $| 1 - 3 \tan x |$ + C
C) - $\frac { 2 } { 3 }$ $( 1 - 3 \tan x ) ^ { 1 / 2 }$ + C
D) $( 1 - 3 \tan x ) ^ { 1 / 2 }$ + C
E) none of these

Quizplus · Accepted Answer

Using the substitution $ u = 1 - 3 \tan x $, the integral simplifies to $-\frac{2}{3} (1 - 3 \tan x)^{1/2} + C$.

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 } }∫(1−3tanx)1/2sec2x​

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