Evaluate the Integral $\int \left( x ^ { 3 } + x ^ { 4 } \right) \sec ^ { 2 } \left( 5 x ^ { 4 } + 4 x ^ { 5 } \right) \mathrm { d } x$

question 1

Multiple Choice

Evaluate the integral. $\int \left( x ^ { 3 } + x ^ { 4 } \right) \sec ^ { 2 } \left( 5 x ^ { 4 } + 4 x ^ { 5 } \right) \mathrm { d } x$

• A) \(\frac { 1 } { 5 } \tan \left( 5 x ^ { 4 } + 4 x ^ { 5 } \right) + C\)
• B) \(\frac { 1 } { 20 } \tan \left( 5 x ^ { 4 } + 4 x ^ { 5 } \right) + C\)
• C) \(\frac { 1 } { 4 } \tan \left( 5 x ^ { 4 } + 4 x ^ { 5 } \right) + C\)
• D) \(\tan \left( 5 x ^ { 4 } + 4 x ^ { 5 } \right) + C\)
• E) \(20 \tan \left( 5 x ^ { 4 } + 4 x ^ { 5 } \right) + C\)

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Definitions:

Yield To Maturity

The total expected return on a bond if held until it matures, including interest payments and capital gains or losses.

Bond A

A classification of bond or debt security with specific features defined by the issuer, such as interest rate and maturity date.

Bond B

A specific category or issue of bonds, which are debt securities issued by corporations or governments to raise funds.

Current Yield

The annual income (interest or dividends) divided by the current price of the security, usually expressed as a percentage.