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Find the integral $\int\frac{4}{2x^{-7}}dx$

Step-by-step Solution

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Final Answer

$\frac{1}{4}x^{8}+C_0$
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Step-by-step Solution

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Cancel the fraction's common factor $2$

$\int\frac{2}{x^{-7}}dx$

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$\int\frac{2}{x^{-7}}dx$

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Learn how to solve differential calculus problems step by step online. Find the integral int(4/(2x^(-7)))dx. Cancel the fraction's common factor 2. 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 (2) 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 7.

Final Answer

$\frac{1}{4}x^{8}+C_0$

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 (4/2x^(-7))dx using partial fractionsSolve integral of (4/2x^(-7))dx using basic integralsSolve integral of (4/2x^(-7))dx using u-substitutionSolve integral of (4/2x^(-7))dx using integration by partsSolve integral of (4/2x^(-7))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{1}{4}x^{8}+C_0$

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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

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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