We can evaluate this integral using integration by substitution, or u-substitution. We pick some part of the integrand to set equal to some variable (such as u, but any variable is an option). Good places to look at first include under a radical or in the denominator. This is not always the case, but it is in this one.
We can set u=1−x
We can substitute these values into our integral. We get:
Which we can rewrite as:
Integrating, we get:
From here you have two options on evaluating for the given limits of integration. You can either choose now to substitute 1−x back in for u and evaluate from 0 to 1, or you can change the limits of integration and evaluate with u. I will demonstrate both options.
Substituting 1−x back in for u,
Changing limits of integration:
u=0 (new upper limit)
u=1 (new lower limit)
Evaluating, we have
Hope this helps!
∫ dx /(x^7 - x) = ∫ dx / x(x^6 - 1) multiply top and bottom with x^5 = ∫ x^5 dx / x^6(x^6 - 1) let x^6 - 1 = u ==> x^6 = u + 1 6x^5 dx = du x^5 dx = du/6
because -8is smaller
where is the
sorry bro my math is weak...
no question dude pls edit
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