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Byju's Answer
Standard IX
Mathematics
Multiplication of Numbers with Square Roots
Prove that ʃd...
Question
Prove that ʃdx/√(1+x²)=log|x+√(x²+1)|
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Q.
If
y
=
x
-
1
log
x
-
1
-
x
+
1
log
x
+
1
, prove that
d
y
d
c
=
log
x
-
1
1
+
x
Q.
Prove that
x
log
y
−
log
z
.
x
log
z
−
log
x
.
x
log
x
−
log
y
=
1
.
Q.
If
y
=
log
x
+
log
x
+
log
x
+
.
.
to
∞
, prove that
2
y
-
1
d
y
d
x
=
1
x
Q.
If
x
x
+
y
x
=
1
, prove that
d
y
d
x
=
-
x
x
1
+
log
x
+
y
x
·
log
y
x
·
y
x
-
1
Q.
If
y
=
log
x
+
1
x
, prove that
d
y
d
x
=
x
-
1
2
x
x
+
1
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