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

## Step-by-step Solution

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

###  Videos

$t^{3}+\frac{1}{4}t^2+C_0$
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## Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

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

$\int3t^2dt+\int\frac{t}{2}dt$
2

The integral $\int3t^2dt$ results in: $t^{3}$

$t^{3}$

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

$\int3t^2dt+\int\frac{t}{2}dt$

Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int(3t^2+t/2)dt. Expand the integral \int\left(3t^2+\frac{t}{2}\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int3t^2dt results in: t^{3}. The integral \int\frac{t}{2}dt results in: \frac{1}{4}t^2. Gather the results of all integrals.

$t^{3}+\frac{1}{4}t^2+C_0$

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

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

### Main topic:

Integrals of Polynomial Functions

~ 0.05 s