Answer:
Step-by-step explanation:
.
It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.
Integration by substitution involves swapping the variable
for another variable which depends on x:
. (We are going to choose
for this question).
The very first step is to choose a suitable substitution. That is, an equation
which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution
.
Your integral contains the term
. The derivative is
and (ignoring the constants) we see
is also in the integral and so the substitution
will unravel this integral!
Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").

Then,
.
The substitution has made this integral is easy to solve!

Finally we can substitute back to get the answer in terms of x:

<span><span><span><span>=−<span><span>2x</span>y</span></span>+<span>3x</span></span>+<span>−<span><span>2x</span>y</span></span></span>+<span>3x
</span></span><span>=<span><span>(<span><span>−<span><span>2x</span>y</span></span>+<span>−<span><span>2x</span>y</span></span></span>)</span>+<span>(<span><span>3x</span>+<span>3x)
=-4xy+6x
</span></span></span></span></span>
And the answer is A. =-4xy+6x
Answer:
D
Step-by-step explanation:
x² + 4 ≤ 2
- x + 4 < 2
Hello from MrBillDoesMath!
Answer:
-10w - 20
Discussion:
5 ( -2w - 4 ) =
5(-2w) - 5(4) =
-10w - 20
Thank you,
MrB
Answer:
8
Step-by-step explanation: