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Q. The value of definite integral $\int\limits_0^2 \frac{x^4+1}{\left(x^4+2\right)^{\frac{3}{4}}} d x$ is equal to

Integrals

Solution:

Let $I=\int\limits_0^2 \frac{\left(x^7+x^3\right)}{\left(x^8+2 x^4\right)^{\frac{3}{4}}} d x ; $ put $\left(x^8+2 x^4\right)=t$ So, we get $I=\frac{1}{2}\left(3^2 \times 2^5\right)^{\frac{1}{4}}=3^{\frac{1}{2}} \times 2^{\frac{1}{4}}=\sqrt{3 \sqrt{2}}$