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Trigonometric Substitution: Complete the Square, Sec
Related Topics
Wize University Calculus 1 Textbook > Integration Techniques
Trigonometric Substitution
4 Activities
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
x
2
−
1
x
2
+
C
\dfrac{\sqrt{x^2-1}}{x^2}+C
x
2
x
2
−
1
+
C
x
2
+
1
x
2
+
C
\dfrac{\sqrt{x^2+1}}{x^2}+C
x
2
x
2
+
1
+
C
x
2
+
1
x
+
C
\dfrac{\sqrt{x^2+1}}{x}+C
x
x
2
+
1
+
C
x
2
−
1
x
+
C
\dfrac{\sqrt{x^2-1}}{x}+C
x
x
2
−
1
+
C
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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
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
.
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: 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