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Find the integral $\int\frac{-5}{x^2}dx$

Step-by-step Solution

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Solution

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Final Answer

$5x^{-1}+C_0$
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Step-by-step Solution

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

$\int-5x^{-2}dx$

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

$\int-5x^{-2}dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int(-5/(x^2))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. The integral of a function times a constant (-5) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -2. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

Final Answer

$5x^{-1}+C_0$

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 (-5/(x^2))dx using partial fractionsSolve integral of (-5/(x^2))dx using basic integralsSolve integral of (-5/(x^2))dx using u-substitutionSolve integral of (-5/(x^2))dx using integration by partsSolve integral of (-5/(x^2))dx using trigonometric substitution

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Function Plot

Plotting: $5x^{-1}+C_0$

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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

How to improve your answer:

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Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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