Calculus Examples

Evaluate the Integral integral of 12/( square root of x)+12 square root of x with respect to x
Step 1
Split the single integral into multiple integrals.
Step 2
Since is constant with respect to , move out of the integral.
Step 3
Apply basic rules of exponents.
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Step 3.1
Use to rewrite as .
Step 3.2
Move out of the denominator by raising it to the power.
Step 3.3
Multiply the exponents in .
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Step 3.3.1
Apply the power rule and multiply exponents, .
Step 3.3.2
Combine and .
Step 3.3.3
Move the negative in front of the fraction.
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
Use to rewrite as .
Step 7
By the Power Rule, the integral of with respect to is .
Step 8
Simplify.
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Step 8.1
Simplify.
Step 8.2
Simplify.
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Step 8.2.1
Combine and .
Step 8.2.2
Combine and .
Step 8.2.3
Multiply by .
Step 8.2.4
Factor out of .
Step 8.2.5
Cancel the common factors.
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Step 8.2.5.1
Factor out of .
Step 8.2.5.2
Cancel the common factor.
Step 8.2.5.3
Rewrite the expression.
Step 8.2.5.4
Divide by .