Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Integral of y^3sin(4*y)*1

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$-\frac{1}{4}y^3\cos\left(4y\right)+\frac{3}{16}y^{2}\sin\left(4y\right)-\frac{3}{128}\left(-4y\cos\left(4y\right)+\sin\left(4y\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(y^{3\:}Sin\:4y\right)dy$
1

Any expression multiplied by $1$ is equal to itself

$\int y^3\sin\left(4y\right)dy$
2

Solve the integral $\int y^3\sin\left(4y\right)dy$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=4y \\ du=4dy\end{matrix}$

Unlock this step-by-step solution!

Answer

$-\frac{1}{4}y^3\cos\left(4y\right)+\frac{3}{16}y^{2}\sin\left(4y\right)-\frac{3}{128}\left(-4y\cos\left(4y\right)+\sin\left(4y\right)\right)+C_0$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

$\int\left(y^{3\:}Sin\:4y\right)dy$

Main topic:

Integration by parts

Used formulas:

6. See formulas

Time to solve it:

~ 0.68 seconds