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Solve the equation with radicals $y=\left(e^x\right)^1nx$

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Solution

Formulas

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Final answer to the problem

$n\left(xe^x-e^x\right)+C_0$
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Step-by-step Solution

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Find the integral

$\int\left(e^x\right)^1nxdx$

Learn how to solve constant rule for differentiation problems step by step online.

$\int\left(e^x\right)^1nxdx$

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Learn how to solve constant rule for differentiation problems step by step online. Solve the equation with radicals y=e^x^1nx. Find the integral. Any expression to the power of 1 is equal to that same expression. The integral of a function times a constant (n) is equal to the constant times the integral of the function. We can solve the integral \int e^x\cdot xdx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x).

Final answer to the problem

$n\left(xe^x-e^x\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of e^x^1ndx using partial fractionsSolve integral of e^x^1ndx using basic integralsSolve integral of e^x^1ndx using u-substitutionSolve integral of e^x^1ndx using integration by partsIntegrate using trigonometric identitiesSolve integral of e^x^1ndx using trigonometric substitution

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Function Plot

Plotting: $n\left(xe^x-e^x\right)+C_0$

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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
D□x
∫
∫◻
|◻|
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

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Main Topic: Constant Rule for Differentiation

The constant rule for differentiation says that the derivative for any constant $k$ is equal to zero.

Used Formulas

See formulas (1)

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