Evaluate the Integral by Using Multiple Substitutions $$\int \frac { 6 \tan ^ { 2 } x \sec ^ { 2 } x } { \left( 3 + \tan ^ { 3 } x \right) ^ { 2 } } d x$$

question 145

Multiple Choice

Evaluate the integral by using multiple substitutions.
- $$\int \frac { 6 \tan ^ { 2 } x \sec ^ { 2 } x } { \left( 3 + \tan ^ { 3 } x \right) ^ { 2 } } d x$$

• A) \(\frac { 2 \tan ^ { 3 } x \sec ^ { 3 } x } { 9 + \tan ^ { 3 } x } + C\)
• B) \(\frac { - 2 } { 3 + \tan ^ { 3 } x } + C\)
• C) \(\frac { 6 x ^ { 2 } } { \left( 3 + x ^ { 3 } \right) ^ { 2 } } + C\)
• D) \(\frac { 2 } { 3 + \cot ^ { 3 } x } + C\)

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Definitions:

White Blood Cells

Cells of the immune system involved in protecting the body against both infectious disease and foreign invaders.

Germinal Center

A region within lymph nodes where mature B cells proliferate, differentiate, and mutate their antibody genes during an immune response.

Efferent Vessel

An efferent vessel is a lymphatic or blood vessel that carries fluid away from an organ or tissue, opposite to an afferent vessel which brings fluid to it.

Afferent Vessel

A vessel that carries blood or lymph fluid towards a particular tissue or organ in the body.