How Do You Integrate 2x sin(x^2) dx?

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SUMMARY

The integral of the function 2x sin(x^2) dx is calculated using the substitution method, specifically with the substitution u = x^2. This leads to the result of -cos(x^2) + C, where C is the constant of integration. The transformation 2x dx = du simplifies the integration process, confirming that the integral can be expressed as ∫ sin(u) du. This method is a standard technique in calculus for handling integrals involving products of polynomials and trigonometric functions.

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may i know how to integ [2x sin (x^2) dx]??the answer is -cos(x^2)

thanx...
 
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use the subsititution u= x^2
 
teng125 said:
may i know how to integ [2x sin (x^2) dx]??the answer is -cos(x^2)
thanx...

\int 2xsin(x^2)dx = \int sin(x^2) dx^2 = -cos(x^2)

The clue is that

2xdx = dx^2

marlon

edit : which is basically the same as what What has stated :)
 
oh...okkk...thanx...
 
teng125 said:
oh...okkk...thanx...
Haha, you don't sound to sure on that. Does it make sense?
 

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