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

Step-by-step Solution

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e
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ln
log
log
lim
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sin
cos
tan
cot
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asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final Answer

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

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1

Apply the formula: $\int e^{\left(a^b\right)}dx$$=\frac{Ei\left(a^b\right)}{\log \left(a\right)}+C$, where $a=2x$ and $b=\frac{1}{2}$

$\frac{Ei\left(\sqrt{2x}\right)}{\log \left(2x\right)}$
2

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

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

Final Answer

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

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Function Plot

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

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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: 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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