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What does converting 1/x^2 to x^-2 help with in integration?
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It simplifies the expression using laws of indices, making it easier to integrate by adding 1 to the power.
What is the general rule for integrating powers of x?
Add one to the power of x, and then divide by the new power.
How do you integrate a constant in an expression?
Include the variable x with the constant and integrate normally.
How do you handle fractions in integration problems?
Use laws of indices to rearrange fractions involving variables, converting expressions like 1/x^2 to x^-2.
What is the integration result of the expression 6x^2 - 5?
2x^3 - 5x + C
What should you do after identifying the power of the variable in an integration problem?
Add one to the power of the variable.
How should you simplify the expression after integrating?
Simplify the fractions and clean up the expression for clarity.
What is a key rule to remember when integrating expressions?
Always add 1 to the power and divide by the new power.
What should you do if an integration problem involves a fraction like 3x^3/4?
Integrate each term separately, simplifying the fraction as necessary, and include the constant of integration.
What is the first step in solving integration problems?
Start by copying the given expression.
How do you ensure clarity in your final integrated expression?
Clean up the expression by simplifying fractions and ensuring all terms are properly integrated.
What is the result of integrating the expression 3x^3/4 - 5x^2/2 + x?
3x^4/8 - 5x^3/6 - ln|x| + C
Why is it important to include the constant of integration (C) in your final answer?
The constant of integration represents an indefinite number of possible constants that could be added to the function, reflecting the general solution to the integral.
How do you integrate the expression 6x^(2+1) - 5x?
What is the integral of x^-2?
-x^-1 + C or -1/x + C
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