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Find the integral $\int\left(x^2+2x+1\right)\sin\left(x\right)dx$

Step-by-step Solution

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Final Answer

$-x^2\cos\left(x\right)-2x\cos\left(x\right)+\cos\left(x\right)+2x\sin\left(x\right)+2\sin\left(x\right)+C_0$
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Step-by-step Solution

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The trinomial $\left(x^2+2x+1\right)$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=2^2-4\left(1\right)\left(1\right) = 0$

Learn how to solve integral calculus problems step by step online.

$\Delta=b^2-4ac=2^2-4\left(1\right)\left(1\right) = 0$

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Learn how to solve integral calculus problems step by step online. Find the integral int(sin(x)(x^2+2x+1))dx. The trinomial \left(x^2+2x+1\right) is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. We can solve the integral \int\left(x+1\right)^{2}\sin\left(x\right)dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x).

Final Answer

$-x^2\cos\left(x\right)-2x\cos\left(x\right)+\cos\left(x\right)+2x\sin\left(x\right)+2\sin\left(x\right)+C_0$

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 sinx(x^2+2x)dx using basic integralsSolve integral of sinx(x^2+2x)dx using u-substitutionSolve integral of sinx(x^2+2x)dx using integration by partsSolve integral of sinx(x^2+2x)dx using tabular integration

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Function Plot

Plotting: $-x^2\cos\left(x\right)-2x\cos\left(x\right)+\cos\left(x\right)+2x\sin\left(x\right)+2\sin\left(x\right)+C_0$

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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: 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

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