Explore and Discuss 1 Formulas 1, 2, and 3 do not provide a formula for the indefinite integral of the function In x. Show that if x > 0, then ∫ ln x d x = x ln x − x + C by differentiating the right-hand side. FORMULAS Indefinite Integrals of Basic Functions For C a constant, 1. ∫ x n d x = x n + 1 n + 1 + C n ≠ − 1 2. ∫ e x d x = e x + C 3. ∫ 1 x d x = ln | x | + C , x ≠ 0
Explore and Discuss 1 Formulas 1, 2, and 3 do not provide a formula for the indefinite integral of the function In x. Show that if x > 0, then ∫ ln x d x = x ln x − x + C by differentiating the right-hand side. FORMULAS Indefinite Integrals of Basic Functions For C a constant, 1. ∫ x n d x = x n + 1 n + 1 + C n ≠ − 1 2. ∫ e x d x = e x + C 3. ∫ 1 x d x = ln | x | + C , x ≠ 0
Solution Summary: The author explains that if x>0 is used, the right hand side is differentiated. Differentiation and integration are reverse operations.
Formulas 1, 2, and 3 do not provide a formula for the indefinite integral of the function In x. Show that if x > 0, then
∫
ln
x
d
x
=
x
ln
x
−
x
+
C
by differentiating the right-hand side.
FORMULAS Indefinite Integrals of Basic Functions
For C a constant,
1.
∫
x
n
d
x
=
x
n
+
1
n
+
1
+
C
n
≠
−
1
2.
∫
e
x
d
x
=
e
x
+
C
3.
∫
1
x
d
x
=
ln
|
x
|
+
C
,
x
≠
0
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Evaluate if it is an indefinite integral or not and why? show your complete solution.
Evaluate the integral in terms of (a) inverse hyperbolic functions and (b) natural logarithms.
4/15
1
1/5 x/1- 9x?
Click the icon to view the table of equations relating inverse hyperbolic functions to logarithmic functions.
4/15
(a)
1/5 x/1- 9x2
(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer.)
rdx =
4/,15
1
(b)
1/5 x/1- 9x?
(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer.)
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY