Substitution - GRE Subject Test: Math
Card 0 of 4
Integrate:
Integrate:
This problem requires U-Substitution. Let 
and find 
.
Notice that the numerator in 
has common factor of 2, 3, or 6. The numerator can be factored so that the 
term can be a substitute. Factor the numerator using 3 as the common factor.
Substitute 
and 
terms, integrate, and resubstitute the 
term.
This problem requires U-Substitution. Let
Notice that the numerator in
Substitute
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Evaluate the following integral:
Evaluate the following integral:
To calculate this integral, we could expand that whole binomial, but it would be very time consuming and a bit of a pain. Instead, let's use u substitution:
Given this:
We can say that
Then, plug it back into our original expression
Evaluate this integral to get
Then, replace u with what we substituted it for to get our final answer. Note because this is an indefinite integral, we need a plus c in it.
To calculate this integral, we could expand that whole binomial, but it would be very time consuming and a bit of a pain. Instead, let's use u substitution:
Given this:
We can say that
Then, plug it back into our original expression
Evaluate this integral to get
Then, replace u with what we substituted it for to get our final answer. Note because this is an indefinite integral, we need a plus c in it.
Compare your answer with the correct one above
Integrate the following using substitution.
Integrate the following using substitution.
Using substitution, we set 
which means its derivative is 
.
Substituting 
for 
, and 
for 
we have:
Now we just integrate:
Finally, we remove our substitution 
to arrive at an expression with our original variable:
Using substitution, we set
Substituting
Now we just integrate:
Finally, we remove our substitution
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Evaluate the following integral:
Evaluate the following integral:
To calculate this integral, we could expand that whole binomial, but it would be very time consuming and a bit of a pain. Instead, let's use u substitution:
Given this:
We can say that
Then, plug it back into our original expression
Evaluate this integral to get
Then, replace u with what we substituted it for to get our final answer. Note because this is an indefinite integral, we need a plus c in it.
To calculate this integral, we could expand that whole binomial, but it would be very time consuming and a bit of a pain. Instead, let's use u substitution:
Given this:
We can say that
Then, plug it back into our original expression
Evaluate this integral to get
Then, replace u with what we substituted it for to get our final answer. Note because this is an indefinite integral, we need a plus c in it.
Compare your answer with the correct one above