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$\int\frac{1}{\sqrt{25-9x^2}}dx$

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Solution

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Final answer to the problem

$\frac{1}{3}\arcsin\left(\frac{3x}{5}\right)+C_0$
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Step-by-step Solution

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First, factor the terms inside the radical by $9$ for an easier handling

$\int\frac{1}{\sqrt{9\left(\frac{25}{9}-x^2\right)}}dx$

Learn how to solve intégrales de fonctions rationnelles problems step by step online.

$\int\frac{1}{\sqrt{9\left(\frac{25}{9}-x^2\right)}}dx$

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Unlock the first 3 steps of this solution

Learn how to solve intégrales de fonctions rationnelles problems step by step online. int(1/((25-9x^2)^(1/2)))dx. First, factor the terms inside the radical by 9 for an easier handling. Taking the constant out of the radical. We can solve the integral \int\frac{1}{3\sqrt{\frac{25}{9}-x^2}}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above.

Final answer to the problem

$\frac{1}{3}\arcsin\left(\frac{3x}{5}\right)+C_0$

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Function Plot

Plotting: $\frac{1}{3}\arcsin\left(\frac{3x}{5}\right)+C_0$

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0
a
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x
y
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(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

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Main Topic: Intégrales de fonctions rationnelles

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