∫ x x ^ 4 a ^ 4 dx Let x ^ 2 =t differentiating w.r.t x, we get 2xdx=dt Now, ∫ x x ^ 4 a ^ 4 dx =∫ 1 2 ...

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Integration of Trigonometric Functions

Solve: ∫xx4-...

Question

Solve: $\int \frac{x}{x^{4} - a^{4}}$

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Solution

$\int \frac{x}{x^{4} - a^{4}} d x L e t x^{2} = t d i f f e r e n t i a t i n g w . r . t x, w e g e t 2 x d x = d t N o w, \int \frac{x}{x^{4} - a^{4}} d x = \int \frac{\frac{1}{2} d t}{t^{2} - (a^{2})^{2}} = \frac{1}{2} \int \frac{d t}{t^{2} - (a^{2})^{2}} = \frac{1}{2} [\frac{1}{{2 a}^{2}} log ∣ ∣ ∣ \frac{t - a^{2}}{t - a^{2}} ∣ ∣ ∣] + C = \frac{1}{{4 a}^{2}} log ∣ ∣ ∣ \frac{x - a^{2}}{x - a^{2}} ∣ ∣ ∣ + C$

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