How do I evaluate $\int \frac{1}{\sqrt{1 - 4 x^{2}}} d x$ $int1/sqrt(1-4x^2)dx$ ?

Question

How do I evaluate $\int \frac{1}{\sqrt{1 - 4 x^{2}}} d x$ $int1/sqrt(1-4x^2)dx$ ?

1 Answer

Impact of this question

3556 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-01-27T17:56:05

To evaluate the integration: $\int \frac{1}{\sqrt{1 - 4 x^{2}}}$ $int1/sqrt(1-4x^2)$

This is very simple. You only need to recall the common integration formula using Trigonometric Substitution.

(Key step) Recall that $\int \frac{1}{\sqrt{a^{2} - u^{2}}} = arcsin (\frac{u}{a}) + C$ $int1/sqrt(a^2 - u^2) = arcsin(u/a) + C$

In this case, you can observe that $a = 1$ $a = 1$ and $u = 2 x$ $u = 2x$ would give you the exactly format

Therefore, the answer for $\int \frac{1}{\sqrt{1 - 4 x^{2}}}$ $int1/sqrt(1-4x^2)$ is $arcsin (2 x) + C$ $arcsin(2x) + C$ or ${sin}^{- 1} (2 x) + C$ $sin^-1(2x) + C$

Feel free to find out the formula sheet online:
[http://www.eeweb.com/tools/math-sheets/images/http://calculus-integrals.png](http://www.eeweb.com/tools/math-sheets/images/calculus-integrals.png)

Science

Math

Humanities

... and beyond

How do I evaluate $\int \frac{1}{\sqrt{1 - 4 x^{2}}} d x$ $int1/sqrt(1-4x^2)dx$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do I evaluate ∫1√1−4x2dxint1/sqrt(1-4x^2)dx?

1 Answer

Related questions

Impact of this question

How do I evaluate $\int \frac{1}{\sqrt{1 - 4 x^{2}}} d x$ $int1/sqrt(1-4x^2)dx$ ?