Question:
Integrate the function: \(\frac {3x}{1+2x^4}\)
Integrate the function: \(\frac {3x}{1+2x^4}\)
Updated On: Oct 4, 2023
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Solution and Explanation
\(Let \ \sqrt 2x^2 = t\)
\(∴ 2\sqrt2x\ dx = dt\)
\(⇒ ∫\frac {3x}{1+2x^4}\ dx = \frac {3}{2\sqrt2} ∫\frac {dt}{1+t^2}\)
\(= \frac {3}{2√2}[tan^{-1} t]+C\)
\(= \frac {3}{2√2}[tan^{-1} (\sqrt 2x^2)]+C\)
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There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
Integrals of Some Particular Functions:
- ∫1/(x2 – a2) dx = (1/2a) log|(x – a)/(x + a)| + C
- ∫1/(a2 – x2) dx = (1/2a) log|(a + x)/(a – x)| + C
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These are tabulated below along with the meaning of each part.
