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Evaluate the integral ∫_ ^ (2x+1)cos(x/2)x.
Related Topics
Wize University Calculus 1 Textbook > Integration Techniques
Integration by Parts
6 Activities
Evaluate the integral
∫
(
2
x
+
1
)
cos
(
x
/
2
)
d
x
\displaystyle\int_{ }^{ }(2x+1)\cos(x/2)\de{x}
∫
(
2
x
+
1
)
cos
(
x
/2
)
d
x
.
4
(
2
x
+
1
)
sin
(
x
/
2
)
+
2
cos
(
x
/
2
)
+
C
4(2x+1)\sin(x/2)+2\cos(x/2)+C
4
(
2
x
+
1
)
sin
(
x
/2
)
+
2
cos
(
x
/2
)
+
C
4
(
2
x
+
1
)
sin
(
x
/
2
)
+
8
cos
(
x
/
2
)
+
C
4(2x+1)\sin(x/2)+8\cos(x/2)+C
4
(
2
x
+
1
)
sin
(
x
/2
)
+
8
cos
(
x
/2
)
+
C
2
(
2
x
+
1
)
sin
(
x
/
2
)
+
2
cos
(
x
/
2
)
+
C
2(2x+1)\sin(x/2)+2\cos(x/2)+C
2
(
2
x
+
1
)
sin
(
x
/2
)
+
2
cos
(
x
/2
)
+
C
2
(
2
x
+
1
)
sin
(
x
/
2
)
+
8
cos
(
x
/
2
)
+
C
2(2x+1)\sin(x/2)+8\cos(x/2)+C
2
(
2
x
+
1
)
sin
(
x
/2
)
+
8
cos
(
x
/2
)
+
C
None of the above
I don't know
Check Submission
More Integration by Parts Questions:
Find
∫
1
e
x
2
ln
x
d
x
\displaystyle\int_1^ex^2\ln\ x\ dx
∫
1
e
x
2
ln
x
d
x
Integration by Parts
Evaluate
∫
x
2
sin
(
π
x
)
d
x
\displaystyle\int x^2 \sin(\pi x) dx
∫
x
2
sin
(
π
x
)
d
x
Integration by Parts
Evaluate
∫
x
2
sin
(
π
x
)
d
x
\displaystyle\int x^2 \sin(\pi x) dx
∫
x
2
sin
(
π
x
)
d
x
Integration by parts
Evaluate
∫
x
sin
x
d
x
\int x\sin x\ dx
∫
x
sin
x
d
x
Find
∫
1
e
x
2
ln
x
d
x
\displaystyle\int_1^ex^2\ln\ x\ dx
∫
1
e
x
2
ln
x
d
x
Practice Question: I by P *
Practice Question
Evaluate
∫
sec
3
x
d
x
{\displaystyle\int}\sec^3x \space\de{x}
∫
sec
3
x
d
x
.
Practice Question: I by P
Practice Question
Evaluate
∫
x
sec
x
tan
x
d
x
{\displaystyle\int}x\sec x\tan x\de{x}
∫
x
sec
x
tan
x
d
x
.
Integration by parts
Evaluate
∫
x
sin
x
d
x
\int x\sin x\ dx
∫
x
sin
x
d
x
Integration by Parts
Evaluate
∫
x
2
sin
(
π
x
)
d
x
\displaystyle\int x^2 \sin(\pi x) dx
∫
x
2
sin
(
π
x
)
d
x
Integration by parts
Evaluate
∫
x
sin
x
d
x
\int x\sin x\ dx
∫
x
sin
x
d
x
Integration by parts
Evaluate
∫
x
sin
x
d
x
\int x\sin x\ dx
∫
x
sin
x
d
x
Integration by Parts
Evaluate
∫
x
2
cos
(
x
)
d
x
\int x ^2\cos (x) \ dx
∫
x
2
cos
(
x
)
d
x
Integration by parts
Evaluate
∫
x
sin
x
d
x
\int x\sin x\ dx
∫
x
sin
x
d
x
Integration by Parts
Evaluate
∫
x
2
sin
(
π
x
)
d
x
\displaystyle\int x^2 \sin(\pi x) dx
∫
x
2
sin
(
π
x
)
d
x
Evaluate the integral
∫
−
1
1
x
2
e
x
d
x
{\displaystyle\int^1_{-1}}x^2e^x\de{x}
∫
−
1
1
x
2
e
x
d
x
.
Evaluate the integral
∫
(
2
x
+
1
)
cos
(
x
/
2
)
d
x
\displaystyle\int_{ }^{ }(2x+1)\cos(x/2)\de{x}
∫
(
2
x
+
1
)
cos
(
x
/2
)
d
x
.
Integration by Parts
Evaluate
∫
x
2
cos
(
x
)
d
x
\int x ^2\cos (x) \ dx
∫
x
2
cos
(
x
)
d
x
Integration by parts
Evaluate
∫
x
sin
x
d
x
\int x\sin x\ dx
∫
x
sin
x
d
x
Practice: Secant with Parts
Q:
\textbf{Q:}
Q:
Evaluate
∫
sec
3
x
d
x
\displaystyle\int\sec^3 x\ dx
∫
sec
3
x
d
x
Find
∫
1
e
x
2
ln
x
d
x
\displaystyle\int_1^ex^2\ln\ x\ dx
∫
1
e
x
2
ln
x
d
x
Find
∫
x
cos
(
2
−
3
x
)
d
x
\displaystyle\int_{ }^{ }x\cos\left(2-3x\right)\ dx
∫
x
cos
(
2
−
3
x
)
d
x
Parts with Exp and Trig, going Round
Integrate
∫
e
3
x
cos
(
5
x
)
d
x
\displaystyle \int e^{3x}\cos(5x)dx
∫
e
3
x
cos
(
5
x
)
d
x
Practice: Parts with Poly and Trig & Substitution
Q:
\textbf{Q:}
Q:
Integrate
∫
x
3
cos
(
x
2
−
1
)
d
x
\displaystyle\int_{ }^{ }x^3\ \cos\left(x^2-1\right)dx
∫
x
3
cos
(
x
2
−
1
)
d
x
Practice: Parts with Poly and Trig, Twice
Q:
\textbf{Q:}
Q:
Integrate
∫
x
2
cos
x
d
x
\displaystyle\int_{ }^{ }x^2\ \cos\ x\ dx
∫
x
2
cos
x
d
x
Evaluate the integral
∫
(
2
x
+
1
)
cos
(
x
/
2
)
d
x
\displaystyle\int_{ }^{ }(2x+1)\cos(x/2)\de{x}
∫
(
2
x
+
1
)
cos
(
x
/2
)
d
x
.
(a)
4
(
2
x
+
1
)
sin
(
x
/
2
)
+
2
cos
(
x
/
2
)
+
C
4(2x+1)\sin(x/2)+2\cos(x/2)+C
4
(
2
x
+
1
)
sin
(
x
/2
)
+
2
cos
(
x
/2
)
+
C
(b)
4
(
2
x
+
1
)
sin
(
x
/
2
)
+
8
cos
(
x
/
2
)
+
C
4(2x+1)\sin(x/2)+8\cos(x/2)+C
4
(
2
x
+
1
)
sin
(
x
/2
)
+
8
cos
(
x
/2
)
+
C
(c)
2
(
2
x
+
1
)
sin
(
x
/
2
)
+
2
cos
(
x
/
2
)
+
C
2(2x+1)\sin(x/2)+2\cos(x/2)+C
2
(
2
x
+
1
)
sin
(
x
/2
)
+
2
cos
(
x
/2
)
+
C
(d)
2
(
2
x
+
1
)
sin
(
x
/
2
)
+
8
cos
(
x
/
2
)
+
C
2(2x+1)\sin(x/2)+8\cos(x/2)+C
2
(
2
x
+
1
)
sin
(
x
/2
)
+
8
cos
(
x
/2
)
+
C
Find
∫
1
e
x
2
ln
x
d
x
\displaystyle\int_1^ex^2\ln\ x\ dx
∫
1
e
x
2
ln
x
d
x
Practice Question
Practice Question
Evaluate
∫
x
sec
x
tan
x
d
x
{\displaystyle\int}x\sec x\tan x\de{x}
∫
x
sec
x
tan
x
d
x
.
Practice Question: I by P *
Practice Question
Evaluate
∫
sec
3
x
d
x
{\displaystyle\int}\sec^3x \space\de{x}
∫
sec
3
x
d
x
.
Practice Question: I by P
Practice Question
Evaluate
∫
x
sec
x
tan
x
d
x
{\displaystyle\int}x\sec x\tan x\de{x}
∫
x
sec
x
tan
x
d
x
.
Evaluate the integral
∫
−
1
1
x
2
e
x
d
x
{\displaystyle\int^1_{-1}}x^2e^x\de{x}
∫
−
1
1
x
2
e
x
d
x
.
Practice Question
Practice Question
Evaluate
∫
x
sec
x
tan
x
d
x
{\displaystyle\int}x\sec x\tan x\de{x}
∫
x
sec
x
tan
x
d
x
.
Evaluate the integral
∫
−
1
1
x
2
e
x
d
x
{\displaystyle\int^1_{-1}}x^2e^x\de{x}
∫
−
1
1
x
2
e
x
d
x
.
Integration by Parts
Evaluate
∫
x
2
sin
(
π
x
)
d
x
\displaystyle\int x^2 \sin(\pi x) dx
∫
x
2
sin
(
π
x
)
d
x
Integration by parts
Find
∫
cos
2
x
d
x
\int \cos^2 x dx
∫
cos
2
x
d
x
Integration Medley
Practice Question
Evauate
∫
arctan
(
x
)
d
x
{\displaystyle\int}\arctan(\sqrt{x})\de{x}
∫
arctan
(
x
)
d
x
.
Evaluate
∫
(
x
ln
x
)
2
d
x
\int_{ }^{ }\left(x\ln x\right)^2dx
∫
(
x
ln
x
)
2
d
x
Practice Question: I by P *
Practice Question
Evaluate
∫
sec
3
x
d
x
{\displaystyle\int}\sec^3x \space\de{x}
∫
sec
3
x
d
x
.
Practice Question: I by P
Practice Question
Evaluate
∫
x
sec
x
tan
x
d
x
{\displaystyle\int}x\sec x\tan x\de{x}
∫
x
sec
x
tan
x
d
x
.
Practice Question: I by P
Practice Question
Find
∫
x
arctan
x
d
x
{\displaystyle \int}x\arctan x\de{x}
∫
x
arctan
x
d
x
.
Integration by Parts
Evaluate
∫
x
2
cos
(
x
)
d
x
\int x ^2\cos (x) \ dx
∫
x
2
cos
(
x
)
d
x
Evaluate
∫
x
2
e
−
x
d
x
\displaystyle\int x^2e^{-x}dx
∫
x
2
e
−
x
d
x
Integration by parts
Evaluate
∫
x
sin
x
d
x
\int x\sin x\ dx
∫
x
sin
x
d
x
Practice Question: I by P
Evaluate
∫
x
sec
x
tan
x
d
x
{\displaystyle\int}x\sec x\tan x\de{x}
∫
x
sec
x
tan
x
d
x
.
Find
∫
π
2
π
x
cos
x
d
x
\displaystyle\int_{\frac{\pi}{2}}^{\pi}\ x\cos\ x\ dx
∫
2
π
π
x
cos
x
d
x
Find
∫
e
x
sin
(
3
x
)
d
x
\displaystyle\int e^x\ \sin\left(3x\right)dx
∫
e
x
sin
(
3
x
)
d
x
Find
∫
1
e
x
2
ln
x
d
x
\displaystyle\int_1^ex^2\ln\ x\ dx
∫
1
e
x
2
ln
x
d
x
Find
∫
x
cos
(
2
−
3
x
)
d
x
\displaystyle\int_{ }^{ }x\cos\left(2-3x\right)\ dx
∫
x
cos
(
2
−
3
x
)
d
x
Practice: Secant with Parts
Q:
\textbf{Q:}
Q:
Evaluate
∫
sec
3
x
d
x
\displaystyle\int\sec^3 x\ dx
∫
sec
3
x
d
x
Parts with Exp and Trig, going Round
Integrate
∫
e
3
x
cos
(
5
x
)
d
x
\displaystyle \int e^{3x}\cos(5x)dx
∫
e
3
x
cos
(
5
x
)
d
x
Practice: Parts with Poly and Trig, Twice
Q:
\textbf{Q:}
Q:
Integrate
∫
x
2
cos
x
d
x
\displaystyle\int_{ }^{ }x^2\ \cos\ x\ dx
∫
x
2
cos
x
d
x
Practice: Parts with Poly and Trig & Substitution
Q:
\textbf{Q:}
Q:
Integrate
∫
x
3
cos
(
x
2
−
1
)
d
x
\displaystyle\int_{ }^{ }x^3\ \cos\left(x^2-1\right)dx
∫
x
3
cos
(
x
2
−
1
)
d
x