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Find the integral $\int3864x\sin\left(30t-30x\right)dx$

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Solution

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Final answer to the problem

$\frac{644}{5}x\cos\left(30t-30x\right)+\frac{322}{75}\sin\left(30t-30x\right)+C_0$
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Step-by-step Solution

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

The integral of a function times a constant ($3864$) is equal to the constant times the integral of the function

Learn how to solve differential equations problems step by step online.

$3864\int x\sin\left(30t-30x\right)dx$

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Learn how to solve differential equations problems step by step online. Find the integral int(3864xsin(30t-30x))dx. The integral of a function times a constant (3864) is equal to the constant times the integral of the function. We can solve the integral \int x\sin\left(30t-30x\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

$\frac{644}{5}x\cos\left(30t-30x\right)+\frac{322}{75}\sin\left(30t-30x\right)+C_0$

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Function Plot

Plotting: $\frac{644}{5}x\cos\left(30t-30x\right)+\frac{322}{75}\sin\left(30t-30x\right)+C_0$

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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
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

How to improve your answer:

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Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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