Try NerdPal! Our new app on iOS and Android

# Find the integral $\int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx$

## Step-by-step Solution

Go!
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
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

### Videos

$x\sin\left(y\right)+y\cos\left(x\right)+C_0$
Got another answer? Verify it here!

## Step-by-step Solution

Problem to solve:

$\int\left(\sin\left(y\right)-y\cdot\sin\left(x\right)\right)dx$

Specify the solving method

1

Expand the integral $\int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int\sin\left(y\right)dx+\int-y\sin\left(x\right)dx$

Learn how to solve integral calculus problems step by step online.

$\int\sin\left(y\right)dx+\int-y\sin\left(x\right)dx$

Learn how to solve integral calculus problems step by step online. Find the integral int(sin(y)-ysin(x))dx. Expand the integral \int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sin\left(y\right)dx results in: x\sin\left(y\right). The integral \int-y\sin\left(x\right)dx results in: y\cos\left(x\right). Gather the results of all integrals.

$x\sin\left(y\right)+y\cos\left(x\right)+C_0$

### Explore different ways to solve this problem

Basic IntegralsIntegration by SubstitutionIntegration by Parts
SnapXam A2

### beta 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
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

$\int\left(\sin\left(y\right)-y\cdot\sin\left(x\right)\right)dx$

### Main topic:

Integral Calculus

~ 0.06 s