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

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##  Final Answer

$\frac{1}{6}t^{3}+t^{4}+C_0$
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##  Step-by-step Solution 

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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

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

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. Integrate 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{1}{6}t^{3}. The integral \int4t^3dt results in: t^{4}. Gather the results of all integrals.

##  Final Answer

$\frac{1}{6}t^{3}+t^{4}+C_0$

##  Explore different ways to solve this problem

SnapXam A2

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7
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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

### Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

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