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Find the integral $\int e^x\sin\left(x\right)dx$

Step-by-step Solution

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sinh
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asinh
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Solution

Formulas

Videos

Final Answer

$\frac{1}{2}e^x\sin\left(x\right)-\frac{1}{2}e^x\cos\left(x\right)+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

$\int\sin\left(x\right)e^xdx$

Specify the solving method

1

We can solve the integral $\int e^x\sin\left(x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Learn how to solve integrals of exponential functions problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Unlock the first 3 steps of this solution!

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(sin(x)e^x)dx. We can solve the integral \int e^x\sin\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

Final Answer

$\frac{1}{2}e^x\sin\left(x\right)-\frac{1}{2}e^x\cos\left(x\right)+C_0$
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Answer Assistant

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Got another answer? Verify it!

Go!
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
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

Useful tips on how to improve your answer:

Similar Problems

Compute the integral

$\int e^x\cos\left(x\right)dx$

Compute the integral

$\int xe^{2x}dx$

Compute the integral

$\int xe^{3x}dx$

Compute the integral

$\int3\cdot e^x\cdot xdx$

Compute the integral

$\int7\cdot e^{8x}\cdot xdx$

Compute the integral

$\int y^2 e^{2y}dy$

Compute the integral

$\int\sin\left(x\right)e^xdx$
$\int\sin\left(x\right)e^xdx$

Main topic:

Integrals of Exponential Functions

Used formulas:

5. See formulas

Time to solve it:

~ 0.11 s

Related topics:

Cyclic integration by partsIntegrals of Exponential FunctionsIntegral CalculusCalculusBasic Differentiation RulesIntegration by PartsIntegration Techniques

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