Question

The value of definite integral $\underset{0}{\overset{2}{\int }}\frac{x^4+1}{{\left(x^4+2\right)}^{\frac{3}{4}}}dx$ is equal to

• A. $\sqrt{2\sqrt{2}}$
• B. $\sqrt{2\sqrt{3}}$
• C. $\sqrt{3\sqrt{2}}$
• D. $\sqrt{3\sqrt{3}}$

Answer 1

Answer: (C)

Let $I=\underset{0}{\overset{2}{\int }}\frac{\left(x^7+x^3\right)}{{\left(x^8+2x^4\right)}^{\frac{3}{4}}}dx;$ put $\left(x^8+2x^4\right)=t$ So, we get $I=\frac{1}{2}{\left(3^2\times 2^5\right)}^{\frac{1}{4}}=3^{\frac{1}{2}}\times 2^{\frac{1}{4}}=\sqrt{3\sqrt{2}}$