# How do you integrate #y = (5x + 3)^6#?

So you've got...

Now, make:

Which means that:

And as a result:

Now, transform:

Integrate:

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To integrate the function ( y = (5x + 3)^6 ), you can use the substitution method. Let ( u = 5x + 3 ), then ( du/dx = 5 ) or ( du = 5dx ). Rearrange to solve for ( dx ), giving ( dx = du/5 ). Now substitute ( u ) and ( du/5 ) into the integral. The integral becomes ( \int u^6 \cdot (1/5) \cdot du ). Now integrate ( u^6 ) with respect to ( u ) to get ( (1/7)u^7 ), then multiply by ( 1/5 ) to get the final answer of ( (1/35)(5x + 3)^7 + C ), where ( C ) is the constant of integration.

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