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# Integrate $\int t\sqrt{2t^2+3}dt$

## Step-by-step Solution

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###  Videos

$\frac{1}{6}\sqrt{\left(2t^2+3\right)^{3}}+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int t\sqrt{2t^2+3}dt$

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1

First, factor the terms inside the radical by $2$ for an easier handling

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

Learn how to solve integrals with radicals problems step by step online.

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

Learn how to solve integrals with radicals problems step by step online. Integrate int(t(2t^2+3)^1/2)dt. First, factor the terms inside the radical by 2 for an easier handling. Taking the constant out of the radical. We can solve the integral \int\sqrt{2}t\sqrt{t^2+\frac{3}{2}}dt by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dt, we need to find the derivative of t. We need to calculate dt, we can do that by deriving the equation above.

$\frac{1}{6}\sqrt{\left(2t^2+3\right)^{3}}+C_0$

##  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(2t^2+3)^1/2)dt using partial fractionsSolve int(t(2t^2+3)^1/2)dt using basic integralsSolve int(t(2t^2+3)^1/2)dt using u-substitutionSolve int(t(2t^2+3)^1/2)dt using integration by partsSolve int(t(2t^2+3)^1/2)dt using trigonometric substitution

SnapXam A2

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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

~ 0.05 s

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