Calculus Examples

Evaluate the Integral integral from 1 to 500 of 13^x-11^x with respect to x+ integral from 2 to 500 of 11^x-13^x with respect to x
Step 1
Evaluate .
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Step 1.1
Split the single integral into multiple integrals.
Step 1.2
The integral of with respect to is .
Step 1.3
Since is constant with respect to , move out of the integral.
Step 1.4
The integral of with respect to is .
Step 1.5
Substitute and simplify.
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Step 1.5.1
Evaluate at and at .
Step 1.5.2
Evaluate at and at .
Step 1.5.3
Simplify.
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Step 1.5.3.1
Evaluate the exponent.
Step 1.5.3.2
Combine the numerators over the common denominator.
Step 1.5.3.3
Evaluate the exponent.
Step 1.5.3.4
Combine the numerators over the common denominator.
Step 1.5.3.5
To write as a fraction with a common denominator, multiply by .
Step 1.5.3.6
To write as a fraction with a common denominator, multiply by .
Step 1.5.3.7
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.5.3.7.1
Multiply by .
Step 1.5.3.7.2
Multiply by .
Step 1.5.3.7.3
Reorder the factors of .
Step 1.5.3.8
Combine the numerators over the common denominator.
Step 2
Evaluate .
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Step 2.1
Split the single integral into multiple integrals.
Step 2.2
The integral of with respect to is .
Step 2.3
Since is constant with respect to , move out of the integral.
Step 2.4
The integral of with respect to is .
Step 2.5
Substitute and simplify.
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Step 2.5.1
Evaluate at and at .
Step 2.5.2
Evaluate at and at .
Step 2.5.3
Simplify.
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Step 2.5.3.1
Raise to the power of .
Step 2.5.3.2
Raise to the power of .
Step 2.5.3.3
To write as a fraction with a common denominator, multiply by .
Step 2.5.3.4
Combine and .
Step 2.5.3.5
Combine the numerators over the common denominator.
Step 2.5.3.6
Combine the numerators over the common denominator.
Step 3
Simplify.
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Step 3.1
To write as a fraction with a common denominator, multiply by .
Step 3.2
Multiply by .
Step 3.3
Combine the numerators over the common denominator.