Solve the integral of logarithmic functions $\int\ln\left(e^{-11y}\right)dy$

Step-by-step Solution

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Final answer to the problem

$-\frac{11}{2}y^2+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
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1

Apply properties of logarithms to expand and simplify the logarithmic expression $\ln\left(e^{-11y}\right)$ inside the integral

$\int-11ydy$

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$\int-11ydy$

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Learn how to solve definite integrals problems step by step online. Solve the integral of logarithmic functions int(ln(e^(-11y)))dy. Apply properties of logarithms to expand and simplify the logarithmic expression \ln\left(e^{-11y}\right) inside the integral. The integral of a function times a constant (-11) is equal to the constant times the integral of the function. Applying the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, in this case n=1. Multiply the fraction and term in -11\cdot \left(\frac{1}{2}\right)y^2.

Final answer to the problem

$-\frac{11}{2}y^2+C_0$

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Function Plot

Plotting: $-\frac{11}{2}y^2+C_0$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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