High School
SAT
SAT Elite 1500
SAT Tutoring
ACT
ACT Elite 33
ACT Tutoring
University
MCAT
MCAT Elite 515
Med-School Admissions
Pre-Med Tutoring
Pre-Med Plus
LSAT
LSAT Elite 170
LSAT Self-Paced
LSAT Tutoring
DAT
DAT Elite
DAT Tutoring
Log in
Get Started for Free
Trigonometric Substitution
Related Topics
Wize University Calculus 1 Textbook > Integration Techniques
Trigonometric Substitution
4 Activities
Find
∫
1
x
2
−
2
x
−
3
d
x
{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}
∫
x
2
−
2
x
−
3
1
d
x
.
ln
∣
x
−
1
2
∣
+
C
\ln\left|\frac{x-1}{2}\right|+C
ln
2
x
−
1
+
C
ln
∣
x
−
1
2
+
(
x
−
1
)
2
−
4
2
∣
+
C
\ln\left|\frac{x-1}{2}+\frac{\sqrt{\left(x-1\right)^2-4}}{2}\right|+C
ln
2
x
−
1
+
2
(
x
−
1
)
2
−
4
+
C
ln
∣
(
x
−
1
)
2
−
4
2
∣
+
C
\ln\left|\frac{\sqrt{\left(x-1\right)^2-4}}{2}\right|+C
ln
2
(
x
−
1
)
2
−
4
+
C
ln
∣
x
−
1
2
+
(
x
−
1
)
2
−
4
2
−
x
2
+
1
2
∣
+
C
\ln\left|\frac{x-1}{2}+\frac{\sqrt{\left(x-1\right)^2-4}}{2}-\frac{x^2+1}{2}\right|+C
ln
2
x
−
1
+
2
(
x
−
1
)
2
−
4
−
2
x
2
+
1
+
C
I don't know
Check Submission
More Trigonometric Substitution Questions:
Trigonometric Substitution
Find
∫
1
x
2
−
2
x
−
3
d
x
{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}
∫
x
2
−
2
x
−
3
1
d
x
.
Practice Question: Trig Sub
Find
∫
1
x
2
−
2
x
−
3
d
x
{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}
∫
x
2
−
2
x
−
3
1
d
x
.
Practice Question: Trig Sub
Find
∫
1
x
2
−
2
x
−
3
d
x
{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}
∫
x
2
−
2
x
−
3
1
d
x
.
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Tan
Evaluate
∫
d
x
x
2
+
4
x
+
8
\displaystyle\int\frac{dx}{\sqrt{x^2+4x+8}}
∫
x
2
+
4
x
+
8
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Practice Question: Trig Sub
Practice Question
Find
∫
1
x
2
−
2
x
−
3
d
x
{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}
∫
x
2
−
2
x
−
3
1
d
x
.
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Practice: Complete the Square, Sec
Q
:
\bf{Q:}
Q
:
Evaluate
∫
x
2
−
4
x
+
2
d
x
\displaystyle\int\sqrt{x^2-4x+2} \ dx
∫
x
2
−
4
x
+
2
d
x
Trigonometric Substitution: Complete the Square, Tan
Evaluate
∫
d
x
x
2
+
4
x
+
8
\displaystyle\int\frac{dx}{\sqrt{x^2+4x+8}}
∫
x
2
+
4
x
+
8
d
x
Practice: Use Sin
Q
:
\bf{Q:}
Q
:
Evaluate
∫
x
+
2
9
−
x
2
d
x
\displaystyle\int\frac{x+2}{\sqrt{9-x^2}}dx
∫
9
−
x
2
x
+
2
d
x
Evaluate
∫
0
4
1
x
2
+
2
x
+
3
d
x
\int_0^4\frac{1}{x^2+2x+3}dx
∫
0
4
x
2
+
2
x
+
3
1
d
x
(a)
2
2
arctan
(
2
2
)
\frac{\sqrt2}{2}\arctan({2\sqrt2})
2
2
arctan
(
2
2
)
(b)
2
2
[
arctan
(
5
2
)
−
arctan
(
1
2
)
]
\frac{\sqrt{2}}{2}\left[\arctan\left(\frac{5}{\sqrt{2}}\right)-\arctan\left(\frac{1}{\sqrt{2}}\right)\right]
2
2
[
arctan
(
2
5
)
−
arctan
(
2
1
)
]
(c)
2
[
arcsin
(
5
2
)
+
arctan
(
1
2
)
]
2\left[\arcsin\left(\frac{5}{\sqrt{2}}\right)+\arctan\left(\frac{1}{\sqrt{2}}\right)\right]
2
[
arcsin
(
2
5
)
+
arctan
(
2
1
)
]
Integration Medley
Practice Question
Evaluate
∫
1
(
x
2
−
6
x
+
11
)
2
d
x
{\displaystyle\int} \frac{1}{(x^2-6x+11)^2}\de{x}
∫
(
x
2
−
6
x
+
11
)
2
1
d
x
.
Evaluate
∫
9
9
x
2
−
2
x
+
6
d
x
\int_{ }^{ }\frac{9}{9x^2-2x+6}dx
∫
9
x
2
−
2
x
+
6
9
d
x
Evaluate
∫
x
2
(
x
2
+
9
)
3
2
d
x
\int_{ }^{ }\frac{x^2}{\left(x^2+9\right)^{\frac{3}{2}}}dx
∫
(
x
2
+
9
)
2
3
x
2
d
x
Evaluate
∫
0
4
1
x
2
+
2
x
+
3
d
x
\int_0^4\frac{1}{x^2+2x+3}dx
∫
0
4
x
2
+
2
x
+
3
1
d
x
Integration Medley
Practice Question
Evaluate
∫
1
(
x
2
−
6
x
+
11
)
2
d
x
{\displaystyle\int} \frac{1}{(x^2-6x+11)^2}\de{x}
∫
(
x
2
−
6
x
+
11
)
2
1
d
x
.
Practice Question: Trig Sub
Practice Question
Find
∫
1
x
2
−
2
x
−
3
d
x
{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}
∫
x
2
−
2
x
−
3
1
d
x
.
Practice: Complete the Square, Sec
Q
:
\bf{Q:}
Q
:
Evaluate
∫
x
2
−
4
x
+
2
d
x
\displaystyle\int\sqrt{x^2-4x+2} \ dx
∫
x
2
−
4
x
+
2
d
x
Practice: Use Sin
Q
:
\bf{Q:}
Q
:
Evaluate
∫
x
+
2
9
−
x
2
d
x
\displaystyle\int\frac{x+2}{\sqrt{9-x^2}}dx
∫
9
−
x
2
x
+
2
d
x
Trigonometric Substitution: Complete the Square, Sec
Evaluate
∫
1
x
2
x
2
−
1
d
x
\displaystyle\int\frac{1}{x^2\sqrt{x^2-1}} \ dx
∫
x
2
x
2
−
1
1
d
x
Trigonometric Substitution: Complete the Square, Tan
Evaluate
∫
d
x
x
2
+
4
x
+
8
\displaystyle\int\frac{dx}{\sqrt{x^2+4x+8}}
∫
x
2
+
4
x
+
8
d
x