1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Integration Using Substitution
Let T= ∫0ln...
Question
Let
T
=
∫
ln
2
0
3
e
3
x
+
2
e
2
x
e
3
x
+
e
2
x
+
1
d
x
, then
e
T
=
p
q
where
p
and
q
are coprime to each other, then find the value of
p
+
q
is
Open in App
Solution
T
=
10
n
2
∫
0
3
e
3
x
+
2
e
2
x
e
3
x
+
e
2
x
+
1
d
x
⇒
Let
e
3
x
+
e
2
x
+
1
=
1
,
x
=
0
,
t
=
3
(
3
e
3
x
+
2
e
2
x
)
d
x
=
d
t
,
x
=
l
n
2
,
t
=
13
T
=
13
∫
3
d
t
t
T
=
l
n
(
t
)
]
13
3
T
=
i
n
(
13
)
−
i
n
(
3
)
T
=
i
n
13
3
and
e
T
=
e
e
i
n
13
3
p
=
13
,
q
=
3
{
∴
9
c
d
(
13
,
3
)
=
1
}
⇒
p
+
q
=
13
+
3
=
16
Suggest Corrections
0
Similar questions
Q.
The probability that f(1) is irrational,is
p
q
(where p and q are coprime then) p+q is equal to
Q.
If the shortest distance of (0,3) from parabola
y
=
x
2
i
s
√
P
q
(where P and q are coprime number), then (p - q) is equal to
Q.
A triangle has sides of length
13
,
30
and
37
. If the radius of the inscribed circle is
p
q
(where p and q are coprime),then the value of
q
p
+
3
is
Q.
If three numbers
(
x
,
y
,
z
)
=
(
2
3
,
7
6
,
8
9
)
and
108
(
L.C.M.
×
H.C.F.
)
=
p
×
q
where
p
,
q
are coprime to each other, then the total number of posiible pairs of
(
p
,
q
)
is
Q.
Three numbers p, q and r are pairwise coprime. If the product of p and q is 629 and that of q and r is 391, then find the value of (p + 2q + r).
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
MATHEMATICS
Watch in App
Explore more
Integration 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
AI Tutor
Textbooks
Question Papers
Install app