Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
The integral
∫
cos
(
log
e
x
)
d
x
\int \cos(\log_e x)\, dx
∫
cos
(
lo
g
e
x
)
d
x
is equal to : (where C is a constant of integration) [JEE-MAIN ONLINE-2019] (1)
x
2
[
sin
(
log
e
x
)
−
cos
(
log
e
x
)
]
+
C
\frac{x}{2}[\sin(\log_e x) - \cos(\log_e x)] + C
2
x
[
sin
(
lo
g
e
x
)
−
cos
(
lo
g
e
x
)]
+
C
(2)
x
2
[
cos
(
log
e
x
)
+
sin
(
log
e
x
)
]
+
C
\frac{x}{2}[\cos(\log_e x) + \sin(\log_e x)] + C
2
x
[
cos
(
lo
g
e
x
)
+
sin
(
lo
g
e
x
)]
+
C
(3)
x
[
cos
(
log
e
x
)
+
sin
(
log
e
x
)
]
+
C
x[\cos(\log_e x) + \sin(\log_e x)] + C
x
[
cos
(
lo
g
e
x
)
+
sin
(
lo
g
e
x
)]
+
C
(4)
x
[
cos
(
log
e
x
)
−
sin
(
log
e
x
)
]
+
C
x[\cos(\log_e x) - \sin(\log_e x)] + C
x
[
cos
(
lo
g
e
x
)
−
sin
(
lo
g
e
x
)]
+
C
Browse the problem library