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

Question

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

Quizplus · Accepted Answer

Let $u = x^3$, then $du = 3x^2 dx$. The integral becomes $\frac{1}{3} \int \sec^2(u) du = \frac{1}{3} \tan(u) + C = \frac{1}{3} \tan(x^3) + C$.

Determine the Integral by Making an Appropriate Substitution ∫x2sec⁡2x3\int x ^ { 2 } \sec ^ { 2 } x ^ { 3 }∫x2sec2x3

Determine the Integral by Making an Appropriate Substitution $\int x ^ { 2 } \sec ^ { 2 } x ^ { 3 }$