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Integrate the function $\frac{\left(x+1\right)^{10}}{\left(4x-16\right)^{11}}$

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{-\left(x+1\right)^{10}}{40\left(4x-16\right)^{10}}+\frac{13563.3680556}{\left(4x-16\right)^{9}}+\frac{6866.4550781}{\left(4x-16\right)^{8}}+\frac{1569.4754464}{\left(4x-16\right)^{7}}+\frac{-213.6230469}{\left(4x-16\right)^{6}}+\frac{-19.2260742}{\left(4x-16\right)^{5}}+\frac{-1.2016296}{\left(4x-16\right)^{4}}+\frac{-\frac{11}{206}}{\left(4x-16\right)^{3}}+\frac{-\frac{1}{582}}{\left(4x-16\right)^{2}}+\frac{-4.29\times 10^{-5}}{4x-16}+2.38\times 10^{-7}\ln\left(4x-16\right)+C_0$
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Step-by-step Solution

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Find the integral

$\int\frac{\left(x+1\right)^{10}}{\left(4x-16\right)^{11}}dx$

Learn how to solve differential equations problems step by step online.

$\int\frac{\left(x+1\right)^{10}}{\left(4x-16\right)^{11}}dx$

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Learn how to solve differential equations problems step by step online. Integrate the function ((x+1)^10)/((4x-16)^11). Find the integral. Rewrite the fraction \frac{\left(x+1\right)^{10}}{\left(4x-16\right)^{11}} inside the integral as the product of two functions: \left(x+1\right)^{10}\frac{1}{\left(4x-16\right)^{11}}. We can solve the integral \int\left(x+1\right)^{10}\frac{1}{\left(4x-16\right)^{11}}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.

Final answer to the problem

$\frac{-\left(x+1\right)^{10}}{40\left(4x-16\right)^{10}}+\frac{13563.3680556}{\left(4x-16\right)^{9}}+\frac{6866.4550781}{\left(4x-16\right)^{8}}+\frac{1569.4754464}{\left(4x-16\right)^{7}}+\frac{-213.6230469}{\left(4x-16\right)^{6}}+\frac{-19.2260742}{\left(4x-16\right)^{5}}+\frac{-1.2016296}{\left(4x-16\right)^{4}}+\frac{-\frac{11}{206}}{\left(4x-16\right)^{3}}+\frac{-\frac{1}{582}}{\left(4x-16\right)^{2}}+\frac{-4.29\times 10^{-5}}{4x-16}+2.38\times 10^{-7}\ln\left(4x-16\right)+C_0$

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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 (((x+1)^10)/((4x-16)^11))dx using partial fractionsSolve integral of (((x+1)^10)/((4x-16)^11))dx using basic integralsSolve integral of (((x+1)^10)/((4x-16)^11))dx using u-substitutionIntegrate using trigonometric identitiesSolve integral of (((x+1)^10)/((4x-16)^11))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{-\left(x+1\right)^{10}}{40\left(4x-16\right)^{10}}+\frac{13563.3680556}{\left(4x-16\right)^{9}}+\frac{6866.4550781}{\left(4x-16\right)^{8}}+\frac{1569.4754464}{\left(4x-16\right)^{7}}+\frac{-213.6230469}{\left(4x-16\right)^{6}}+\frac{-19.2260742}{\left(4x-16\right)^{5}}+\frac{-1.2016296}{\left(4x-16\right)^{4}}+\frac{-\frac{11}{206}}{\left(4x-16\right)^{3}}+\frac{-\frac{1}{582}}{\left(4x-16\right)^{2}}+\frac{-4.29\times 10^{-5}}{4x-16}+2.38\times 10^{-7}\ln\left(4x-16\right)+C_0$

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x
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(◻)
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◻/◻
/
÷
◻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: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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