Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP
Topics

Step-by-step Solution

Integral of $\frac{x^3}{\sqrt{16-x^2}}$ with respect to x

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
|◻|
=
>
<
>=
<=
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

$x^3\arcsin\left(\frac{x}{4}\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x^3}{\sqrt{16-x^2}}dx$
1

Apply the well-known integration formula: $\int\frac{1}{\sqrt{a^2-x^2}}dx = \arcsin\left(\frac{x}{a}\right)$

$x^3\arcsin\left(\frac{x}{4}\right)$
2

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$x^3\arcsin\left(\frac{x}{4}\right)+C_0$

Answer

$x^3\arcsin\left(\frac{x}{4}\right)+C_0$

Problem Analysis

$\int\frac{x^3}{\sqrt{16-x^2}}dx$

Time to solve it:

~ 0.09 seconds