Using the log Rule for integration In Exercises 13–30, find the indefinite integral. See Examples 4, 5, and 6.
∫
1
x
(
ln
x
)
2
d
x
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.
Rewrite the expressions in Exercises 5–8 in terms of exponentials and simplify the results as much as you can.
5. 2 cosh (ln x)
6. sinh (2 ln x)
7. cosh 5x + sinh 5x
8. cosh 3x - sinh 3x
In Exercises 139–142, determine whether each statement is true
or false. If the statement is false, make the necessary change(s) to
produce a true statement.
log, 8 8
140. log(-100) = -2
139.
log, 4
141. The domain of f(x) = log, x is (-0∞, ∞).
4
142. log, x is the exponent to which b must be raised to obtain x.
Calculus 11th Edition by Ron Larson
Chapter 5 Section 5.4: Exponential Functions: Differentiation and Integration
Finding an Equation of a Tangent Line: In Exercises 55–62, find an equation of the tangent line to the graph of the function at the given point.
Please show all work and explain steps, thank you!
Chapter 5 Solutions
Bundle: Calculus: An Applied Approach, Loose-Leaf Version, 10th + WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term
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