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!

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