Find the integral $\int\sin\left(4\right)x^3\cos\left(4x\right)dx$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{4}\sin\left(4\right)x^3\sin\left(4x\right)+\sin\left(4\right)\cdot \frac{3}{16}x^{2}\cos\left(4x\right)+\sin\left(4\right)\cdot \left(-\frac{3}{32}\right)x\sin\left(4x\right)+\frac{-3\sin\left(4\right)\cos\left(4x\right)}{128}+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by parts
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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The integral of a function times a constant ($\sin\left(4\right)$) is equal to the constant times the integral of the function

$\sin\left(4\right)\int x^3\cos\left(4x\right)dx$

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$\sin\left(4\right)\int x^3\cos\left(4x\right)dx$

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Unlock the first 3 steps of this solution

Learn how to solve integral calculus problems step by step online. Find the integral int(cos(4x)sin(4)x^3)dx. The integral of a function times a constant (\sin\left(4\right)) is equal to the constant times the integral of the function. We can solve the integral \int x^3\cos\left(4x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v.

Final answer to the problem

$\frac{1}{4}\sin\left(4\right)x^3\sin\left(4x\right)+\sin\left(4\right)\cdot \frac{3}{16}x^{2}\cos\left(4x\right)+\sin\left(4\right)\cdot \left(-\frac{3}{32}\right)x\sin\left(4x\right)+\frac{-3\sin\left(4\right)\cos\left(4x\right)}{128}+C_0$

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Function Plot

Plotting: $\frac{1}{4}\sin\left(4\right)x^3\sin\left(4x\right)+\sin\left(4\right)\cdot \frac{3}{16}x^{2}\cos\left(4x\right)+\sin\left(4\right)\cdot -\frac{3}{32}x\sin\left(4x\right)+\frac{-3\sin\left(4\right)\cos\left(4x\right)}{128}+C_0$

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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

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 (7)

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