# High School Math : Integrals

## Example Questions

### Example Question #66 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

To find the indefinite integral of our equation, we can use the reverse power rule.

To use the reverse power rule, we raise the exponent of the  by one and then divide by that new exponent.

Remember that, when taking the integral, we treat constants as that number times  since anything to the zero power is . For example, treat  as .

When taking an integral, be sure to include a  at the end of everything.  stands for "constant". Since taking the derivative of a constant whole number will always equal , we include the  to anticipate the possiblity of the equation actually being  or  instead of just  .

### Example Question #67 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

To find the indefinite integral of our equation, we can use the reverse power rule.

To use the reverse power rule, we raise the exponent of the  by one and then divide by that new exponent.

When taking an integral, be sure to include a  stands for "constant". Since taking the derivative of a constant whole number will always equal , we include the  to anticipate the possiblity of the equation actually being  or  instead of just  .

### Example Question #68 : Calculus Ii — Integrals

What is the indefinite integral of ?

Undefined

Explanation:

To find the indefinite integral of our equation, we can use the reverse power rule.

To use the reverse power rule, we raise the exponent of the  by one and then divide by that new exponent.

Remember that, when taking the integral, we treat constants as that number times , since anything to the zero power is . Treat  as .

When taking an integral, be sure to include a  stands for "constant". Since taking the derivative of a constant whole number will always equal , we include the  to anticipate the possiblity of the equation actually being  or  instead of just  .

### Example Question #69 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

is a special function.

The indefinite integral is .

Even though it is a special function, we still need to include a  stands for "constant". Since taking the derivative of a constant whole number will always equal , we include the  to anticipate the possiblity of the equation actually being  or  instead of just  .

### Example Question #70 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

To solve this problem, we can use the anti-power rule or reverse power rule. We raise the exponent on the variables by one and divide by the new exponent.

For this problem, we'll treat  as  since anything to the zero power is one.

Since the derivative of any constant is , when we take the indefinite integral, we add a  to compensate for any constant that might be there.

From here we can simplify.

### Example Question #71 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

To solve this problem, we can use the anti-power rule or reverse power rule. We raise the exponent on the variables by one and divide by the new exponent.

For this problem, we'll treat  as  since anything to the zero power is one.

Since the derivative of any constant is , when we take the indefinite integral, we add a  to compensate for any constant that might be there.

From here we can simplify.

### Example Question #72 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

To solve this problem, we can use the anti-power rule or reverse power rule. We raise the exponent on the variables by one and divide by the new exponent.

For this problem, we'll treat  as  since anything to the zero power is one.

Since the derivative of any constant is , when we take the indefinite integral, we add a  to compensate for any constant that might be there.

From here we can simplify.

### Example Question #73 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

To find the indefinite integral, we can use the reverse power rule: we raise the exponent by one and then divide by our new exponent.

Remember when taking the indefinite integral to include a  to cover any potential constants.

Simplify.

### Example Question #74 : Calculus Ii — Integrals

What is the indefinite integral of ?

Explanation:

To find the indefinite integral, we can use the reverse power rule: we raise the exponent by one and then divide by our new exponent.

We are going to treat  as  since anything to the zero power is one.

Remember when taking the indefinite integral to include a  to cover any potential constants.

Simplify.

### Example Question #75 : Calculus Ii — Integrals

What is the indefinite integral of ?