Find the integral $\int\frac{27e^{\left(\sqrt{x+1}\right)}}{2\sqrt{x+1}}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{27}{2}Ei\left(\sqrt{x+1}\right)+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
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Take out the constant $27$ from the integral

$27\int\frac{e^{\left(\sqrt{x+1}\right)}}{2\sqrt{x+1}}dx$

Learn how to solve integrals of exponential functions problems step by step online.

$27\int\frac{e^{\left(\sqrt{x+1}\right)}}{2\sqrt{x+1}}dx$

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Unlock the first 3 steps of this solution

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int((27e^(x+1)^(1/2))/(2(x+1)^(1/2)))dx. Take out the constant 27 from the integral. Take the constant \frac{1}{2} out of the integral. Multiply the fraction and term in 27\cdot \left(\frac{1}{2}\right)\int\frac{e^{\left(\sqrt{x+1}\right)}}{\sqrt{x+1}}dx. The integral \int\frac{e^{\left(\sqrt{x+1}\right)}}{\sqrt{x+1}}dx is called 'exponential integral' and is non-elementary. The formula for the exponential integral is: \int\frac{e^x}{x}=Ei(x), where Ei is a special function on the complex plane.

Final answer to the problem

$\frac{27}{2}Ei\left(\sqrt{x+1}\right)+C_0$

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Plotting: $\frac{27}{2}Ei\left(\sqrt{x+1}\right)+C_0$

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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: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

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