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Antiderivatives: Inverse Trigonometric Functions
Related Topics
Wize University Calculus 1 Textbook > Integrals
Antiderivatives of Inverse Trig Functions
3 Activities
Find
∫
2
4
−
t
2
d
t
\int_{ }^{ }\frac{2}{\sqrt{4-t^2}}dt
∫
4
−
t
2
2
d
t
.
2
arcsin
(
t
2
)
+
C
2\arcsin\left(\frac{t}{2}\right)+C
2
arcsin
(
2
t
)
+
C
2
arcsin
(
t
)
+
C
2\arcsin\left(t\right)+C
2
arcsin
(
t
)
+
C
2
arcsin
(
2
t
)
+
C
2\arcsin\left(2t\right)+C
2
arcsin
(
2
t
)
+
C
4
arcsin
(
t
)
+
C
4\arcsin\left(t\right)+C
4
arcsin
(
t
)
+
C
4
arcsin
(
t
2
)
+
C
4\arcsin\left(\frac{t}{2}\right)+C
4
arcsin
(
2
t
)
+
C
I don't know
Check Submission
More Antiderivatives of Inverse Trig Functions Questions:
Integration Medley
Practice Question
Evaluate
∫
x
4
+
1
x
2
+
1
d
x
{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}
∫
x
2
+
1
x
4
+
1
d
x
.
Evaluate the integral
∫
x
4
+
1
x
2
+
1
d
x
\displaystyle\int\frac{x^4+1}{x^2+1}dx
∫
x
2
+
1
x
4
+
1
d
x
.
Find the value of the definite integral
∫
π
/
6
π
/
3
(
sec
x
+
tan
x
)
sec
x
d
x
\displaystyle \int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx
∫
π
/6
π
/3
(
sec
x
+
tan
x
)
sec
x
d
x
.
Evaluate the indefinite integral
∫
6
x
+
e
−
6
x
−
3
x
2
+
1
d
x
\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx
∫
6
x
+
e
−
6
x
−
x
2
+
1
3
d
x
.
Evaluate the indefinite integral
∫
6
x
+
e
−
6
x
−
3
x
2
+
1
d
x
\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx
∫
6
x
+
e
−
6
x
−
x
2
+
1
3
d
x
.
Practice: Definite Integral (~F2017 Final Q26)
Practice: Definite Integral
Evaluate
∫
0
3
1
9
+
x
2
+
2
x
ln
2
d
x
\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx
∫
0
3
9
+
x
2
1
+
2
x
ln
2
d
x
.
Integration Medley
Practice Question
Evaluate
∫
x
4
+
1
x
2
+
1
d
x
{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}
∫
x
2
+
1
x
4
+
1
d
x
.
Integration Medley
Practice Question
Evaluate
∫
x
4
+
1
x
2
+
1
d
x
{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}
∫
x
2
+
1
x
4
+
1
d
x
.
Integration Medley
Practice Question
Evaluate
∫
x
4
+
1
x
2
+
1
d
x
{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}
∫
x
2
+
1
x
4
+
1
d
x
.
Evaluate
∫
−
1
0
d
x
1
−
x
2
\int_{-1}^0\frac{dx}{\sqrt{1-x^2}}
∫
−
1
0
1
−
x
2
d
x
Integration Medley
Practice Question
Evaluate
∫
x
4
+
1
x
2
+
1
d
x
{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}
∫
x
2
+
1
x
4
+
1
d
x
.
Practice: Definite Integral
Evaluate
∫
0
3
1
9
+
x
2
+
2
x
ln
2
d
x
\displaystyle \int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx
∫
0
3
9
+
x
2
1
+
2
x
ln
2
d
x
.
Antiderivatives: Inverse Trigonometric Functions
Evaluate
d
d
u
cos
−
1
u
sin
−
1
u
\displaystyle \frac{\text{d}}{\text{d}u} \frac{\cos^{-1}u}{\sin^{-1}u}
d
u
d
sin
−
1
u
cos
−
1
u
. It is not necessary to simplify.
Evaluate the integral
∫
x
4
+
1
x
2
+
1
d
x
\displaystyle\int\frac{x^4+1}{x^2+1}dx
∫
x
2
+
1
x
4
+
1
d
x
.
Find the value of the definite integral
∫
π
/
6
π
/
3
(
sec
x
+
tan
x
)
sec
x
d
x
\displaystyle \int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx
∫
π
/6
π
/3
(
sec
x
+
tan
x
)
sec
x
d
x
.
Find the indefinite integral
∫
(
1
1
+
x
+
1
1
+
x
2
)
d
x
\int(\frac{1}{1+x}+\frac{1}{1+x^2})dx
∫
(
1
+
x
1
+
1
+
x
2
1
)
d
x
.
Evaluate the indefinite integral
∫
6
x
+
e
−
6
x
−
3
x
2
+
1
d
x
\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx
∫
6
x
+
e
−
6
x
−
x
2
+
1
3
d
x
.
Evaluate
∫
−
1
0
d
x
1
−
x
2
\int_{-1}^0\frac{dx}{\sqrt{1-x^2}}
∫
−
1
0
1
−
x
2
d
x
Practice: Definite Integral
Practice: Definite Integral
Evaluate
∫
0
3
1
9
+
x
2
+
2
x
ln
2
d
x
\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx
∫
0
3
9
+
x
2
1
+
2
x
ln
2
d
x
.