Evaluate: #int_1^2 1/(x^3+x) dx# ?
4 Answers
Use partial fractions.
Explanation:
# = [lnx-1/2ln(x^2+1)]_1^2#
# = (ln2-1/2ln5)-(0-1/2ln2)#
# = 3/2ln2-1/2ln5 = 1/2ln(8/5)#
(E) None of the above.
Note
Typically we think about trigonometric substitution if we have a quadratic.
So the
Use partial fractions to get rid of the cubic.
It then turns out that we don't need trigonometric substitution.
Added Note
See the answer by Mason M. for a solution by trigonometric substitution.
Integral
Explanation:
Solving the indefinite integral.
[Partial fractions]
[Linearity]
Solving
Solving
Let
Undo substitution
Applying bounds
Option (E) None of the above.
Explanation:
Let us rewrite the given integral as,
We solve it without Trig. Substn.
We subst.
Further,
Clearly, the Right Choice is Option (E) None of the above.
Enjoy Maths.!
Let's try the trigonometric substitution
So, plugging these in, the integral becomes:
If
Then:
Which equals all the other provided answers given on Socratic and shows that the answer to your question is (E), none of the above.