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Example Questions
Example Question #2163 : Calculus
Evaluate the following indefinite integral:
In this problem we use a "u substitution" to account for the function inside of the parentheses. The steps for a "u-sub" are as follows:
1. Set the function equal to u, take the derivative of both sides, and solve for dx:
2. Substitute each of the x values for u values in the integral then solve accordingly:
3. Put the x values back into the equation and add "C" to get the final answer:
Example Question #91 : Equations
Evaluate the following indefinite integral:
To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:
1. Set u equal to the x equation in parentheses, take the derivative, and solve:
2. Replace x values with u values and integrate accordingly:
3. Put the original x equation back in for u and add "C":
Example Question #92 : Integral Expressions
Evaluate the following indefinite integral:
To solve this problem we have to use a u substitution. We also need to remember our properties of trig functions. A "u-sub" is done by using the following steps:
1. Set u equal to the x equation in parentheses, take the derivative, and solve:
2. Replace x values with u values and integrate accordingly:
3. Put the original x equation back in for u and add "C":
Example Question #1141 : Functions
Evaluate the following indefinite integral:
To solve this problem, all we have to remember is that the integral of e doesn't change. That gives us the following:
Example Question #91 : Equations
Evaluate the following indefinite integral:
To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:
1. Set u equal to the x equation in parentheses, take the derivative, and solve:
2. Replace x values with u values and integrate accordingly:
3. Put the original x equation back in for u and add "C":
Example Question #95 : Integral Expressions
Evaluate the following indefinite integral:
To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:
1. Set u equal to the x equation in parentheses, take the derivative, and solve:
2. Replace x values with u values and integrate accordingly:
3. Put the original x equation back in for u and add "C":
Example Question #2172 : Calculus
Evaluate the following indefinite integral:
To solve this integral, we use the power rule for the first term:
And use the laws of trig functions for the second term:
We can combine these terms and add our "C" to get the final answer:
Example Question #2173 : Calculus
Evaluate the following indefinite integral:
To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:
1. Set u equal to the x equation in parentheses, take the derivative, and solve:
2. Replace x values with u values and integrate accordingly:
3. Put the original x equation back in for u and add "C":
Example Question #92 : Writing Equations
Evaluate the following indefinite integral:
To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:
1. Set u equal to the x equation in parentheses, take the derivative, and solve:
2. Replace x values with u values and integrate accordingly:
3. Put the original x equation back in for u and add "C":
Example Question #99 : Integral Expressions
Evaluate the following indefinite integral:
To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:
1. Set u equal to the x equation in parentheses, take the derivative, and solve:
2. Replace x values with u values and integrate accordingly:
3. Put the original x equation back in for u and add "C":
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