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Solve the trigonometric integral $\int5\sin\left(5x-3\right)dx$

Step-by-step Solution

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Final Answer

$-\cos\left(5x-3\right)+C_0$
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Step-by-step Solution

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The integral of a function times a constant ($5$) is equal to the constant times the integral of the function

$5\int\sin\left(5x-3\right)dx$

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

$5\int\sin\left(5x-3\right)dx$

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(5sin(5x-3))dx. The integral of a function times a constant (5) is equal to the constant times the integral of the function. We can solve the integral \int\sin\left(5x-3\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 5x-3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

Final Answer

$-\cos\left(5x-3\right)+C_0$

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 5sin(5x-3)dx using basic integralsSolve integral of 5sin(5x-3)dx using u-substitutionSolve integral of 5sin(5x-3)dx using integration by partsSolve integral of 5sin(5x-3)dx using tabular integration

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1
2
3
4
5
6
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: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

3. See formulas

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