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CALCULUS ONE TEST ONE Pt.2 NAME(in ink) SHOW ALL CALCULATIONS. SIMPLIFY ANSWERS. Due Oct. 25, 2012. 1. Find Page 1 of 2. Dy in the following problems Write expressions in factored form if possible.
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How to fill out sec5x tan4x dx

Steps to fill out sec5x tan4x dx:
01
Start by understanding the terms: sec5x stands for the secant of 5x, and tan4x represents the tangent of 4x.
02
Identify the integral you want to solve, which is ∫sec5x tan4x dx.
03
Apply the integration by parts technique. To do this, use the following formula: ∫u dv = uv - ∫v du.
04
Choose which function to differentiate and which function to integrate. In this case, it is recommended to let u = sec5x and dv = tan4x dx.
05
Calculate du by taking the derivative of u with respect to x. In this case, du will be 5 sec5x tan5x dx.
06
Integrate dv by integrating tan4x dx. This can be done by using the substitution method or referring to a table of integrals. The result should be ∫tan4x dx = -1/3 ln|cos4x|.
07
Now, substitute the values of u, v, du, and the integral of dv into the integration by parts formula:
∫sec5x tan4x dx = sec5x (-1/3 ln|cos4x|) - ∫(-1/3 ln|cos4x|)(5 sec5x tan5x dx).
01
Simplify the expression further if needed, using algebraic rules and properties.
02
If the integral in the equation is still unsolvable, consider applying other integration techniques such as trigonometric identities or substitution.
03
Finally, you should have a solution for the integral ∫sec5x tan4x dx.
Who needs sec5x tan4x dx?
01
Students studying calculus or advanced mathematics often encounter integrals like ∫sec5x tan4x dx in their coursework.
02
Engineers, physicists, and other professionals who work with mathematical models or need to analyze functions may come across this integral in their work.
03
Individuals who are curious about learning and expanding their knowledge of mathematics might find the concept of sec5x tan4x dx intriguing and want to explore it further.
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What is sec5x tan4x dx?
Sec5x tan4x dx is an indefinite integral that involves the trigonometric functions secant and tangent.
Who is required to file sec5x tan4x dx?
Math students and individuals studying calculus may encounter sec5x tan4x dx in their studies.
How to fill out sec5x tan4x dx?
Sec5x tan4x dx can be solved using integration techniques for trigonometric functions.
What is the purpose of sec5x tan4x dx?
The purpose of sec5x tan4x dx is to find the integral of the given expression involving secant and tangent functions.
What information must be reported on sec5x tan4x dx?
The solution or value of the indefinite integral for sec5x tan4x dx must be reported.
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