Determine the integral by making an appropriate substitution.
-$\int \tan ^ { 2 } x \sec ^ { 2 } x d x$ Use the substitution u = tan x.
A) $\frac { \tan ^ { 2 } x } { 2 }$ + C
B) sec x tan x + C
C) $\frac { \sec ^ { 2 } x } { 2 }$ + C
D) $\frac { \tan ^ { 3 } x } { 3 }$ + C
E) none of these

Question

Determine the integral by making an appropriate substitution. 
-$\int \tan ^ { 2 } x \sec ^ { 2 } x d x$   Use the substitution u = tan x.
A) $\frac { \tan ^ { 2 } x } { 2 }$ + C
B) sec x tan x + C
C) $\frac { \sec ^ { 2 } x } { 2 }$ + C
D) $\frac { \tan ^ { 3 } x } { 3 }$ + C
E) none of these

Quizplus · Accepted Answer

Using the substitution $u = \tan x$, we get $du = \sec^2 x dx$. Substituting these into the integral gives $\int u^2 du$, which integrates to $\frac{u^3}{3} + C$, or $\frac{\tan^3 x}{3} + C$.

Determine the Integral by Making an Appropriate Substitution ∫tan⁡2xsec⁡2xdx\int \tan ^ { 2 } x \sec ^ { 2 } x d x∫tan2xsec2xdx

Determine the Integral by Making an Appropriate Substitution $\int \tan ^ { 2 } x \sec ^ { 2 } x d x$