Answer:
(e) csc x − cot x − ln(1 + cos x) + C
(c) 0
Step-by-step explanation:
(e) ∫ (1 + sin x) / (1 + cos x) dx
Split the integral.
∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx
Multiply top and bottom of first integral by the conjugate, 1 − cos x.
∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx
Pythagorean identity.
∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx
Divide.
∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx
Integrate.
csc x − cot x − ln(1 + cos x) + C
(c) ∫₋₇⁷ erf(x) dx
= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx
The error function is odd (erf(-x) = -erf(x)), so:
= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx
= 0
For one since since the angles should add up to 180 degrees we must start by adding 55 and 25 which is 80 so 180-80=100 which means c is 100 degrees and for the other I'm going with C
Subtract $145-$53 and you will get 92.
Then divide 92 by 23 and you get 4.
The answer is 4 because when you subract 53 from 145 you are seeing how much you paid without the fee.
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![5^ \frac{2}{5}= \sqrt[5]{5^2}= \sqrt[5]{25}](https://tex.z-dn.net/?f=5%5E%20%5Cfrac%7B2%7D%7B5%7D%3D%20%5Csqrt%5B5%5D%7B5%5E2%7D%3D%20%5Csqrt%5B5%5D%7B25%7D%20%20)