Try now NerdPal! Our new app on iOS and Android

Find the integral $\int8x^2\cos\left(x^3\right)dx$

Step-by-step Solution

Go!
Math mode
Text mode
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

Final Answer

$\frac{8}{3}\sin\left(x^3\right)+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

$\int8x^2\cos\left(x^3\right)dx$

Specify the solving method

1

The integral of a function times a constant ($8$) is equal to the constant times the integral of the function

$8\int x^2\cos\left(x^3\right)dx$

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

$8\int x^2\cos\left(x^3\right)dx$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve integral calculus problems step by step online. Find the integral int(8x^2cos(x^3))dx. The integral of a function times a constant (8) is equal to the constant times the integral of the function. We can solve the integral \int x^2\cos\left(x^3\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x^3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

Final Answer

$\frac{8}{3}\sin\left(x^3\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(8x^2cos(x^3))dx using basic integralsSolve int(8x^2cos(x^3))dx using u-substitutionSolve int(8x^2cos(x^3))dx using integration by partsSolve int(8x^2cos(x^3))dx using tabular integration

Give us your feedback!

SnapXam A2
Answer Assistant

beta
Got a different 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

How to improve your answer:

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Including multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android app.

Join 500k+ students in problem solving.

Subscription. Cancel anytime.
Have a promo code?
Pay $2.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account
3-Month Special Plan
One-time payment of $2.97 USD.
Without automatic renewal.
Create an Account