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Find the integral $\int7\cdot e^7x\sin\left(3x\right)dx$

Step-by-step Solution

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Solution

Final answer to the problem

$e^7\cdot \left(-\frac{7}{3}\right)x\cos\left(3x\right)+\frac{7\cdot e^7\sin\left(3x\right)}{9}+C_0$
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Step-by-step Solution

How should I solve this problem?

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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 ($7$) is equal to the constant times the integral of the function

$7\int e^7x\sin\left(3x\right)dx$

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$7\int e^7x\sin\left(3x\right)dx$

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Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Find the integral int(7e^7xsin(3x))dx. The integral of a function times a constant (7) is equal to the constant times the integral of the function. The integral of a function times a constant (e^7) is equal to the constant times the integral of the function. We can solve the integral \int x\sin\left(3x\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.

Final answer to the problem

$e^7\cdot \left(-\frac{7}{3}\right)x\cos\left(3x\right)+\frac{7\cdot e^7\sin\left(3x\right)}{9}+C_0$

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Function Plot

Plotting: $e^7\cdot -\frac{7}{3}x\cos\left(3x\right)+\frac{7\cdot e^7\sin\left(3x\right)}{9}+C_0$

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5
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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
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

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