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The Integration by parts exercise appears under the Integral calculus math mission on Khan Academy. This exercise shows how to take the product of integrals using the inverse product rule.

## Types of Problems Edit

There are three types of problems in this exercise:

1. Evaluate the Indefinite value: The student is asked to find the equation for the values of the integral using the inverse product rule.

2. Evaluate the definite integral: The student is asked to find the value of the integral by using the inverse product rule.

3. Find the formula of the integral that will lower power on x: The student is asked to find the formula of the integral by substituting the values and using the inverse product rule.

## Strategies Edit

Knowledge of derivatives, antiderivatives, and the inverse product rule are encouraged to ensure success on this exercise.

1. The inverse product rule states:

$\int f(x)g'(x) dx$ = $f(x)g(x)- \int f'(x)g(x) dx$

$\int u dv$ = $uv - \int v du$

2. When solving natural logarithm, you can make the function into two functions by putting the number one outside the parenthesis.

Example: $\int ln(x) dx$ = $\int ln(x)1 dx$

3. When writing the formula for the product rule, it is helpful to write the values of the of the derivatives and integrals of each function first.

4. All of the questions are multiple choice, so elimination can be used to find the correct answer.

5. The derivative and integral of $e^x$ is $e^x$(excluding the constant)

6. If the integral of the inverse product rule doesn't have a value, you can value out the equation.

Example: $2 \int(e^x)(cosx) dx$ = $e^xsinx+e^xcosx$

$\int(e^x)(cosx)$ = $\frac{e^xsinx+e^xcosx}{2}$