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

Answer 1

Emilia Aguilar

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!

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Answer 2

Cameron Alexander

To integrate ( \int x^2 \cdot 3^{5x^3 + 1} ) using substitution, we can let ( u = 5x^3 + 1 ). Then, differentiate ( u ) with respect to ( x ) to find ( du ). Afterwards, we can express the integral in terms of ( u ), making it easier to integrate.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.