Find the integral $\pi +\int_{-1}^{2}\left(\left(x+4\right)^2-\left(x^2+2\right)^2\right)dx$

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Final answer to the problem

$\frac{248.7079633}{5}-\frac{160}{15}$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by trigonometric substitution
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Expand the integral $\int_{-1}^{2}\left(\left(x+4\right)^2-\left(x^2+2\right)^2\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\pi +\int_{-1}^{2}\left(x+4\right)^2dx+\int_{-1}^{2}-\left(x^2+2\right)^2dx$

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$\pi +\int_{-1}^{2}\left(x+4\right)^2dx+\int_{-1}^{2}-\left(x^2+2\right)^2dx$

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Learn how to solve integral calculus problems step by step online. Find the integral pi+int((x+4)^2-(x^2+2)^2)dx&-1&2. Expand the integral \int_{-1}^{2}\left(\left(x+4\right)^2-\left(x^2+2\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int-\left(x^2+2\right)^2dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get.

Final answer to the problem

$\frac{248.7079633}{5}-\frac{160}{15}$

Exact Numeric Answer

$39.074926$

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Plotting: $\frac{248.7079633}{5}-\frac{160}{15}$

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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

How to improve your answer:

Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

See formulas (5)

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