Integrate ? 4x^3 cos x^4 dx

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Answer 1 · 2018-04-06T05:12:53

#int4x^3cos(x^4)dx=sin(x^4)+C#

So, we want

#int4x^3cos(x^4)dx#

For this problem, a simple substitution suffices.

#u=x^4#

#(du)/dx=4x^3#

#du=4x^3dx#

#4x^3dx# shows up in our integral in that exact form, so, this substitution is valid.

Rewrite, realizing that this is an elementary integral:

#intcosudu=sinu+C#

Recalling that #u=x^4:#

#int4x^3cos(x^4)dx=sin(x^4)+C#