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Integrate $\int t\sqrt{t^2-4}dt$

Step-by-step Solution

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Final Answer

$\frac{1}{3}\sqrt{\left(t^2-4\right)^{3}}+C_0$
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Step-by-step Solution

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We can solve the integral $\int t\sqrt{t^2-4}dt$ by applying integration method of trigonometric substitution using the substitution

$t=2\sec\left(\theta \right)$

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

$t=2\sec\left(\theta \right)$

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Learn how to solve integrals with radicals problems step by step online. Integrate int(t(t^2-4)^1/2)dt. We can solve the integral \int t\sqrt{t^2-4}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. Substituting in the original integral, we get. Simplifying.

Final Answer

$\frac{1}{3}\sqrt{\left(t^2-4\right)^{3}}+C_0$

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 integral of t(t^2-4)^0.5dt using partial fractionsSolve integral of t(t^2-4)^0.5dt using basic integralsSolve integral of t(t^2-4)^0.5dt using u-substitutionSolve integral of t(t^2-4)^0.5dt using integration by partsSolve integral of t(t^2-4)^0.5dt using trigonometric substitution

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Function Plot

Plotting: $\frac{1}{3}\sqrt{\left(t^2-4\right)^{3}}+C_0$

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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:

Main Topic: Integrals with Radicals

Integrals with radicals are those integrals that contain a radical (square root, cubic, etc.) in the numerator or denominator of the integral.

Used Formulas

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