Rizzi – Calc BC
 Sometimes
we have to integrate more
complicated functions
 We
need to recognize the chain rule pattern
in these functions:
2
𝑥 +1
2
1 2
= 𝑥 +1
3
2𝑥 𝑑𝑥
3
+𝐶
5cos(5𝑥) 𝑑𝑥
= sin 5𝑥 + 𝐶
 Sometimes
these bad boys get way too
complicated, though…
2𝑥 − 1𝑑𝑥
1
= 2𝑥 − 1
3
3
2
+𝐶
2
sin 3𝑥 𝑐𝑜𝑠3𝑥
1 3
= sin 3𝑥 + 𝐶
9
𝑑𝑥
4𝑥
−
1 − 2𝑥 2
𝑑𝑥
2
1
=−
+
𝐶
1 − 2𝑥 2
2
𝑥
+1
2 𝑑𝑥
 Complete
as many problems on the
worksheet as you can
I
will check 10 random problems tomorrow.
You will receive a HW score out of 5 points.
 Your
answer must be TOTALLY correct for you
to earn the point. Include all work on a
separate piece of paper, but put answers on
main worksheet.
 NOT
ALL REQUIRE U-SUB. ALSO SKIP #908
Rizzi – Calc BC
1
𝑥
2
𝑥
+1
0
15
=
8
3 𝑑𝑥
5
1
𝑥
2𝑥 − 1
16
=
3
𝑑𝑥
0
𝑥 + 2 𝑑𝑥
−5
= 6.5
 For
some functions, it’s easy to find the
antiderivative, but evaluating it over a
closed interval is
impossible:
1
1
𝑑𝑥
2
−1 𝑥