How do you integrate #int x^2*3^(5x^3+1)# using substitution?

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Answer 1 · 2017-02-05T03:12:33

The integral equals #3^(5x^3 + 1)/(15ln3) + C#

Let #u = 5x^3 + 1#. Then #du = 15x^2dx -> dx = (du)/(15x^2)#.

#=>intx^2 * 3^u * (du)/(15x^2)#

#=>1/15int 3^u du#

Use the formula #inta^udu = a^u/lna#

#=>1/15(3^u/ln3) + C#

#=>3^(5x^3 + 1)/(15ln3) + C#

Hopefully this helps!