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Integrate $\int\left(x^2+4x+\frac{-23}{x^2-4}+x+3\right)dx$

Step-by-step Solution

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Final Answer

$\frac{x^{3}}{3}+\frac{5}{2}x^2-\frac{23}{4}\ln\left(x-2\right)+\frac{23}{4}\ln\left(x+2\right)+3x+C_0$
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Step-by-step Solution

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Simplify the expression inside the integral

$\int x^2dx+\int5xdx+\int\frac{-23}{x^2-4}dx+\int3dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int x^2dx+\int5xdx+\int\frac{-23}{x^2-4}dx+\int3dx$

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Learn how to solve trigonometric integrals problems step by step online. Integrate int(x^2+4x-23/(x^2-4)x+3)dx. Simplify the expression inside the integral. The integral \int x^2dx results in: \frac{x^{3}}{3}. The integral \int5xdx results in: \frac{5}{2}x^2. The integral \int\frac{-23}{x^2-4}dx results in: \frac{23}{4}\ln\left(x+2\right)-\frac{23}{4}\ln\left(x-2\right).

Final Answer

$\frac{x^{3}}{3}+\frac{5}{2}x^2-\frac{23}{4}\ln\left(x-2\right)+\frac{23}{4}\ln\left(x+2\right)+3x+C_0$

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

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Function Plot

Plotting: $\frac{x^{3}}{3}+\frac{5}{2}x^2-\frac{23}{4}\ln\left(x-2\right)+\frac{23}{4}\ln\left(x+2\right)+3x+C_0$

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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: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

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