Find the indefinite integral. $$\int \frac { \cot \left( 13 / z ^ { 2 } \right) } { z ^ { 3 } } d z$$
A) $\frac { 1 } { 13 } \ln \left| \sin \left( 13 / z ^ { 2 } \right) \right| + C$
B) $- \frac { 1 } { 26 } \ln | \sin ( 13 / z ) | + C$
C) $- \frac { 1 } { 13 } \ln \left| \sin \left( 13 / z ^ { 2 } \right) \right| + C$
D) $- \frac { 1 } { 26 } \ln \left| \sin \left( 13 / z ^ { 2 } \right) \right| + C$
E) $\frac { 1 } { 26 } \ln \left| \sin \left( 13 / z ^ { 2 } \right) \right| + C$

Question

Quizplus · Accepted Answer

To solve the integral $\int \frac { \cot \left( 13 / z ^ { 2 } \right) } { z ^ { 3 } } d z$, use substitution. Let $u = 13/z^2$, then $du = -26/z^3 dz$. The integral becomes $-\frac{1}{26}\int \cot(u) du = -\frac{1}{26} \ln|\sin(u)| + C$, which corresponds to choice D when reverting back to the original variable.

Find the Indefinite Integral ∫cot⁡(13/z2)z3dz\int \frac { \cot \left( 13 / z ^ { 2 } \right) } { z ^ { 3 } } d z∫z3cot(13/z2)​dz

Find the Indefinite Integral $\int \frac { \cot \left( 13 / z ^ { 2 } \right) } { z ^ { 3 } } d z$