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Ramanujan Integral

In this video, I evaluate the integral from 0 to infinity of e^(-x^3) sin(x^3) dx using a very nice formula due to Ramanujan, which relates integrals of the form x^s f(x) with a sort of power series of f. Enjoy! Note: I would like to thank philosophicalmath for this idea, you should check out his blog: https://philosophicalmath.wordpress.com/

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Integral of e^-x ln(x) from 0 to infinity
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Integral of e^-x ln(x) from 0 to infinity

Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.
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Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.

life changing integration by parts trick
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life changing integration by parts trick

Math for fun, sin(z)=2
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Math for fun, sin(z)=2

Ramanujan's master theorem is insanely overpowered!!! example using the Fresnel integrals
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Ramanujan's master theorem is insanely overpowered!!! example using the Fresnel integrals

the most famous Ramanujan sum 1+2+3+...=-1/12
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the most famous Ramanujan sum 1+2+3+...=-1/12

Ramanujan's integral is ridiculous!
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Ramanujan's integral is ridiculous!

Best Explanation of Gradient, Divergence and Curl
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Best Explanation of Gradient, Divergence and Curl

Ramanujan Summation
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Ramanujan Summation

Einstein OBSERVED Ramanujan's Work And Saw Mathematics That Shouldn't Exist
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Einstein OBSERVED Ramanujan's Work And Saw Mathematics That Shouldn't Exist

Ramanujan's Master Theorem: One to Rule Them All
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Ramanujan's Master Theorem: One to Rule Them All

William Dunham, A tribute to Euler
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William Dunham, A tribute to Euler

the complex derivative is strange...
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the complex derivative is strange...

COOL Dirichlet Integral 😎
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COOL Dirichlet Integral 😎

Using Ramanujan's Master Theorem to solve complicated integrals!
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Using Ramanujan's Master Theorem to solve complicated integrals!

Learn Mathematics Like Ramanujan Did
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Learn Mathematics Like Ramanujan Did

How Ramanujan proved his master theorem
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How Ramanujan proved his master theorem

The Obviously True Theorem No One Can Prove
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The Obviously True Theorem No One Can Prove

The Integral Explained Better Than School Ever Did
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The Integral Explained Better Than School Ever Did

Feynman's Technique of Integration
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Feynman's Technique of Integration

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