Mathematics - Calculus
Not what you're looking for?
1. Write arctan ...
2. Evaluate the integrals ...
3.Use integration by parts twice to find ...
[See the attached questions file.]
Purchase this Solution
Solution Summary
The expert evaluates integration by parts twice to find the solution functions. Neat, step-by-step solution is provided.
Solution Preview
The solution file is attached.
Integration
u = arctan x and dv = 1 dx
udv = uv - v du
arctan x dx = arctan x * x - [x/(1 + x^2)]dx
= x * arctan x - (1/2) dt/t, where t = 1 + x^2
= x * arctan x - (1/2) ln t + C
= x * arctan x - (1/2) ln(1 + x^2) + C
(2) u = t and dv = sin t dt
udv = uv - v du
t sin t dt = t(- cos t) - (- cos t)dt = -t cos t + cos t dt = -t cos t + sin t + C
(4) u = t and dv = e^(5t) dt
udv = uv - v du
t e^(5t) dt = t[e^(5t) /5] - [{e^(5t) /5} dt = (1/5) t e^(5t) - (1/5) e^(5t) dt
= (1/5) t e^(5t) - (1/25) e^(5t) + C
(18) u = z and dv = e^-z dz
udv = uv - v du
z e^-z dz = z(-e^-z) - [-e^-z] dz = -z e^-z + e^-z dz = -z e^-z - e^-z + C
...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.