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Integrate $\int\left(\frac{x-4}{x^2+3x}-10\right)dx$

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Solution

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Final Answer

$\frac{7}{3}\ln\left(x+3\right)-\frac{4}{3}\ln\left(x\right)-10x+C_0$
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Step-by-step Solution

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Expand the integral $\int\left(\frac{x-4}{x^2+3x}-10\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int\frac{x-4}{x^2+3x}dx+\int-10dx$

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

$\int\frac{x-4}{x^2+3x}dx+\int-10dx$

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Learn how to solve integrals of polynomial functions problems step by step online. Integrate int((x-4)/(x^2+3x)-10)dx. Expand the integral \int\left(\frac{x-4}{x^2+3x}-10\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x-4}{x^2+3x}dx results in: -\frac{4}{3}\ln\left(x\right)+\frac{7}{3}\ln\left(x+3\right). Gather the results of all integrals. The integral \int-10dx results in: -10x.

Final Answer

$\frac{7}{3}\ln\left(x+3\right)-\frac{4}{3}\ln\left(x\right)-10x+C_0$

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 ((x-4)/(x^2+3x)-10)dx using partial fractionsSolve integral of ((x-4)/(x^2+3x)-10)dx using basic integralsSolve integral of ((x-4)/(x^2+3x)-10)dx using u-substitutionSolve integral of ((x-4)/(x^2+3x)-10)dx using integration by partsSolve integral of ((x-4)/(x^2+3x)-10)dx using trigonometric substitution

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Plotting: $\frac{7}{3}\ln\left(x+3\right)-\frac{4}{3}\ln\left(x\right)-10x+C_0$

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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: Integrals of Polynomial Functions

Integrals of polynomial functions.

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