Order these steps in the u-substitution process:
-
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Substitute back
x
\displaystyle {x}
x
's for
u
\displaystyle {u}
u
's everywhere in your answer.
-
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Compute
d
u
=
d
u
d
x
d
x
.
\displaystyle {d}{u}={\frac{{{d}{u}}}{{{\left.{d}{x}\right.}}}}{\left.{d}{x}\right.}.
d
u
=
d
x
d
u
d
x
.
-
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Integrate the new
u
\displaystyle {u}
u
-integral, if possible. (If you still can't integrate it, go back and try a different choice for
u
\displaystyle {u}
u
.)
-
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Translate all your
x
\displaystyle {x}
x
's into
u
\displaystyle {u}
u
's everywhere in the integral, including the
d
x
\displaystyle {\left.{d}{x}\right.}
d
x
.
-
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Let
u
\displaystyle {u}
u
be some part of the integrand. A good first choice is
one step inside the messiest bit.
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