Integral of (e^(1/2))/(x^2)

\int\frac{e^{\frac{1}{2}}}{x^2}dx

Go!
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x
y
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2

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

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$\frac{-\sqrt[3]{7}}{x}+C_0$

Step by step solution

Problem

$\int\frac{e^{\frac{1}{2}}}{x^2}dx$
1

Calculate the square root of $e$

$\int\frac{\sqrt[3]{7}}{x^2}dx$
2

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int\sqrt[3]{7}x^{-2}dx$
3

Taking the constant out of the integral

$\sqrt[3]{7}\int x^{-2}dx$
4

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$\sqrt[3]{7}\cdot\frac{x^{-1}}{-1}$
5

Simplify the fraction

$-\sqrt[3]{7}x^{-1}$
6

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$-\sqrt[3]{7}\cdot\frac{1}{x}$
7

Apply the formula: $a\frac{1}{x}$$=\frac{a}{x}$, where $a=-\sqrt[3]{7}$

$\frac{-\sqrt[3]{7}}{x}$
8

Add the constant of integration

$\frac{-\sqrt[3]{7}}{x}+C_0$

Answer

$\frac{-\sqrt[3]{7}}{x}+C_0$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.24 seconds

Views:

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