$\text { Find the integral } \int \frac { t } { t ^ { 4 } + 81 } d t \text {. }$

question 27

Multiple Choice

$\text { Find the integral } \int \frac { t } { t ^ { 4 } + 81 } d t \text {. }$

• A) \(\frac { 1 } { 18 } \arctan 9 t ^ { 2 } d t + C\)
• B) \(\frac { 1 } { 18 } \arctan \frac { t ^ { 2 } } { 9 } d t + C\)
• C) \(\arctan \frac { t ^ { 2 } } { 81 } d t + C\)
• D) \(\frac { 1 } { 9 } \arctan 81 t ^ { 2 } d t + C\)
• E) \(\arctan \frac { t ^ { 2 } } { 9 } d t + C\)

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Definitions:

Unilateral Mistake

A misunderstanding where one party to a contract is mistaken about a basic assumption on which the contract is based.

Rescinded

Revoked, canceled, or repealed, usually by official or formal action.

Public Trustee

A government official or department appointed to manage the estates, property, or financial affairs of individuals unable to do so themselves due to incapacity, absence, or death.

Doctrine of Mistake

Legal principles that allow a contract to be declared void if both parties were under a mutual misunderstanding about a key fact of the agreement.