Calculus Examples

Evaluate the Integral integral of (x^2-8)/(8x) with respect to x
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Divide by .
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Step 2.1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
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Step 2.2
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 2.3
Multiply the new quotient term by the divisor.
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Step 2.4
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 2.5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 2.6
Pull the next term from the original dividend down into the current dividend.
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Step 2.7
The final answer is the quotient plus the remainder over the divisor.
Step 3
Split the single integral into multiple integrals.
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
Since is constant with respect to , move out of the integral.
Step 7
Multiply by .
Step 8
The integral of with respect to is .
Step 9
Simplify.