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# Find the integral $\int\left(\frac{t^2}{2}+4t^3\right)dt$

## Step-by-step Solution

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###  Videos

$\frac{t^{3}}{6}+t^{4}+C_0$
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## Step-by-step Solution

Problem to solve:

$\int\left(\frac{t^2}{2}+4t^3\right)dt$

Specify the solving method

1

Expand the integral $\int\left(\frac{t^2}{2}+4t^3\right)dt$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int\frac{t^2}{2}dt+\int4t^3dt$
2

The integral $\int\frac{t^2}{2}dt$ results in: $\frac{t^{3}}{6}$

$\frac{t^{3}}{6}$

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

$\int\frac{t^2}{2}dt+\int4t^3dt$

Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int((t^2)/2+4t^3)dt. Expand the integral \int\left(\frac{t^2}{2}+4t^3\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{t^2}{2}dt results in: \frac{t^{3}}{6}. The integral \int4t^3dt results in: t^{4}. Gather the results of all integrals.

$\frac{t^{3}}{6}+t^{4}+C_0$

##  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((t^2)/2+4t^3)dt using partial fractionsSolve int((t^2)/2+4t^3)dt using basic integralsSolve int((t^2)/2+4t^3)dt using u-substitutionSolve int((t^2)/2+4t^3)dt using integration by partsSolve int((t^2)/2+4t^3)dt using trigonometric substitution
SnapXam A2

### beta Got a different answer? Verify it!

Go!
1
2
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5
6
7
8
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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

$\int\left(\frac{t^2}{2}+4t^3\right)dt$

### Main topic:

Integrals of Polynomial Functions

~ 0.07 s