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Simplify $\sqrt[8]{\left(\sqrt{3v^2+\pi }\right)^{7}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $\frac{7}{8}$
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$\int v\sqrt[16]{\left(3v^2+\pi \right)^{7}}dv$
Learn how to solve integrals with radicals problems step by step online. Integrate int(v(3v^2+pi)^1/2^7/8)dv. Simplify \sqrt[8]{\left(\sqrt{3v^2+\pi }\right)^{7}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals \frac{7}{8}. First, factor the terms inside the radical by 3 for an easier handling. Taking the constant out of the radical. We can solve the integral \int1.617114v\sqrt[16]{\left(v^2+\frac{\pi}{3}\right)^{7}}dv by applying integration method of trigonometric substitution using the substitution.