Basic Math Examples

Simplify (e^36+1)/4
e36+14e36+14
Step 1
Rewrite e36e36 as (e12)3(e12)3.
(e12)3+14(e12)3+14
Step 2
Rewrite 11 as 1313.
(e12)3+134(e12)3+134
Step 3
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2)a3+b3=(a+b)(a2ab+b2) where a=e12a=e12 and b=1b=1.
(e12+1)((e12)2-e121+12)4(e12+1)((e12)2e121+12)4
Step 4
Simplify.
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Step 4.1
Rewrite e12e12 as (e4)3(e4)3.
((e4)3+1)((e12)2-e121+12)4((e4)3+1)((e12)2e121+12)4
Step 4.2
Rewrite 11 as 1313.
((e4)3+13)((e12)2-e121+12)4((e4)3+13)((e12)2e121+12)4
Step 4.3
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2)a3+b3=(a+b)(a2ab+b2) where a=e4a=e4 and b=1b=1.
(e4+1)((e4)2-e41+12)((e12)2-e121+12)4(e4+1)((e4)2e41+12)((e12)2e121+12)4
Step 4.4
Simplify.
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Step 4.4.1
Multiply the exponents in (e4)2(e4)2.
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Step 4.4.1.1
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
(e4+1)(e42-e41+12)((e12)2-e121+12)4(e4+1)(e42e41+12)((e12)2e121+12)4
Step 4.4.1.2
Multiply 44 by 22.
(e4+1)(e8-e41+12)((e12)2-e121+12)4(e4+1)(e8e41+12)((e12)2e121+12)4
(e4+1)(e8-e41+12)((e12)2-e121+12)4(e4+1)(e8e41+12)((e12)2e121+12)4
Step 4.4.2
Multiply -11 by 11.
(e4+1)(e8-e4+12)((e12)2-e121+12)4(e4+1)(e8e4+12)((e12)2e121+12)4
Step 4.4.3
One to any power is one.
(e4+1)(e8-e4+1)((e12)2-e121+12)4(e4+1)(e8e4+1)((e12)2e121+12)4
(e4+1)(e8-e4+1)((e12)2-e121+12)4(e4+1)(e8e4+1)((e12)2e121+12)4
Step 4.5
Multiply -11 by 11.
(e4+1)(e8-e4+1)((e12)2-e12+12)4(e4+1)(e8e4+1)((e12)2e12+12)4
(e4+1)(e8-e4+1)((e12)2-e12+12)4(e4+1)(e8e4+1)((e12)2e12+12)4
Step 5
Simplify each term.
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Step 5.1
Multiply the exponents in (e12)2(e12)2.
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Step 5.1.1
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
(e4+1)(e8-e4+1)(e122-e12+12)4(e4+1)(e8e4+1)(e122e12+12)4
Step 5.1.2
Multiply 1212 by 22.
(e4+1)(e8-e4+1)(e24-e12+12)4(e4+1)(e8e4+1)(e24e12+12)4
(e4+1)(e8-e4+1)(e24-e12+12)4(e4+1)(e8e4+1)(e24e12+12)4
Step 5.2
One to any power is one.
(e4+1)(e8-e4+1)(e24-e12+1)4(e4+1)(e8e4+1)(e24e12+1)4
(e4+1)(e8-e4+1)(e24-e12+1)4(e4+1)(e8e4+1)(e24e12+1)4
Step 6
The result can be shown in multiple forms.
Exact Form:
(e4+1)(e8-e4+1)(e24-e12+1)4(e4+1)(e8e4+1)(e24e12+1)4
Decimal Form:
1.0778078810151.077807881015
 [x2  12  π  xdx ]  x2  12  π  xdx