Evalute the integrals using the given substitution

[(ln x)^6dx] / x given u = ln x

x^4 sinx^5dx given u = x^5

For the first problem, u = ln(x) => du = dx/x => dx = x*du

=> int(ln(x)^6*dx)/x) = int(u^6*du) = u^7/7 + C

Plugging u = ln(x) back in...

= ln(x)^7/7 + C

For the second problem, u = x^5 => du = 5*x^4*dx => dx = du/(5*x^4)

=> int(x^4*sin(x^5)*dx) = int((sin(u)/5)*du) = int(sin(u)*du)/5 = -cos(u)/5 + C

Plugging u = x^5 back in...

= -cos(x^5)/5 + C

I believe this is how it's done. Hope this helps!

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