1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Differentiation Using Substitution
Evaluate the ...
Question
Evaluate the following integrals:
∫
e
2
x
sin
3
x
+
1
d
x
Open in App
Solution
We
have
,
I
=
∫
e
2
x
sin
3
x
+
1
d
x
Let
the
first
function
be
sin
3
x
+
1
and
the
second
function
be
e
2
x
.
First
we
find
the
integral
of
the
second
function
,
i
.
e
.
,
∫
e
2
x
dx
.
∫
e
2
x
dx
=
1
2
e
2
x
Now
,
using
integration
by
parts
,
we
get
I
=
sin
3
x
+
1
∫
e
2
x
d
x
-
∫
d
sin
3
x
+
1
d
x
∫
e
2
x
d
x
d
x
=
1
2
sin
3
x
+
1
e
2
x
-
3
2
∫
cos
3
x
+
1
e
2
x
d
x
=
1
2
sin
3
x
+
1
e
2
x
-
3
2
cos
3
x
+
1
∫
e
2
x
d
x
-
∫
d
cos
3
x
+
1
d
x
∫
e
2
x
d
x
d
x
=
1
2
sin
3
x
+
1
e
2
x
-
3
2
1
2
cos
3
x
+
1
e
2
x
+
3
2
∫
sin
3
x
+
1
e
2
x
d
x
=
1
2
sin
3
x
+
1
e
2
x
-
3
4
cos
3
x
+
1
e
2
x
-
9
4
I
+
c
I
+
9
4
I
=
1
2
sin
3
x
+
1
e
2
x
-
3
4
cos
3
x
+
1
e
2
x
+
c
13
4
I
=
e
2
x
2
sin
3
x
+
1
-
3
2
cos
3
x
+
1
+
c
I
=
2
13
e
2
x
sin
3
x
+
1
-
3
2
cos
3
x
+
1
+
c
=
e
2
x
13
2
sin
3
x
+
1
-
3
cos
3
x
+
1
+
c
Hence
,
∫
e
2
x
sin
3
x
+
1
d
x
=
e
2
x
13
2
sin
3
x
+
1
-
3
cos
3
x
+
1
+
c
Suggest Corrections
0
Similar questions
Q.
Evaluate the following integrals:
∫
-
1
1
2
x
+
1
d
x
Q.
Evaluate the following integrals:
∫
-
3
3
x
+
1
d
x
Q.
Evaluate the following integrals:
∫
x
x
2
+
1
x
-
1
d
x
Q.
Evaluate the following integrals:
∫
0
3
3
x
-
1
d
x
Q.
Evaluate the following integrals:
∫
x
3
+
x
+
1
x
2
-
1
d
x
∫
x
3
+
x
+
1
x
2
-
1
d
x
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Method of Substitution
MATHEMATICS
Watch in App
Explore more
Differentiation Using Substitution
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app
