Evaluate the Integral $$\int \frac { 7 d x } { \left( x ^ { 2 } + 2 x + 2 \right) ^ { 2 } }$$

question 50

Multiple Choice

Evaluate the integral. $$\int \frac { 7 d x } { \left( x ^ { 2 } + 2 x + 2 \right) ^ { 2 } }$$

• A) \(\frac { 1 } { 2 } \left( \tan ( x + 1 ) + \frac { 17 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• B) \(\frac { 1 } { 2 } \left( \tan ^ { - 1 } ( x + 2 ) + \frac { 7 } { x ^ { 2 } + 2 } \right) + C\)
• C) \(\frac { 1 } { 2 } \left( \tan ^ { - 1 } ( x + 7 ) + \frac { 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• D) \(\frac { 7 } { 2 } \left( \tan ( x + 2 ) + \frac { x + 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• E) \(\frac { 7 } { 2 } \left( \tan ^ { - 1 } ( x + 1 ) + \frac { x + 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)

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Definitions:

Initiator tRNA

The transfer RNA that recognizes the start codon on mRNA and initiates protein synthesis by bringing the first amino acid to the ribosome.

Amino Acid

Organic compounds that combine to form proteins, serving as the building blocks of life.

Leucine

an essential amino acid used in the biosynthesis of proteins, important for muscle repair and growth.

Poly-A Tail

The string of adenine nucleotides added to the 3' end of a newly synthesized pre-mRNA molecule, playing a role in mRNA stability and translation.