Calculus Examples

Find the Antiderivative (5-4x^3+2x^6)/(x^6)
Step 1
Write as a function.
Step 2
The function can be found by finding the indefinite integral of the derivative .
Step 3
Set up the integral to solve.
Step 4
Move out of the denominator by raising it to the power.
Step 5
Multiply the exponents in .
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Step 5.1
Apply the power rule and multiply exponents, .
Step 5.2
Multiply by .
Step 6
Expand .
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Step 6.1
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Use the power rule to combine exponents.
Step 6.4
Subtract from .
Step 6.5
Use the power rule to combine exponents.
Step 6.6
Subtract from .
Step 6.7
Anything raised to is .
Step 6.8
Multiply by .
Step 6.9
Reorder and .
Step 7
Split the single integral into multiple integrals.
Step 8
Since is constant with respect to , move out of the integral.
Step 9
By the Power Rule, the integral of with respect to is .
Step 10
Simplify.
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Step 10.1
Combine and .
Step 10.2
Move to the denominator using the negative exponent rule .
Step 11
Since is constant with respect to , move out of the integral.
Step 12
By the Power Rule, the integral of with respect to is .
Step 13
Simplify.
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Step 13.1
Combine and .
Step 13.2
Move to the denominator using the negative exponent rule .
Step 14
Apply the constant rule.
Step 15
Simplify.
Step 16
The answer is the antiderivative of the function .