exact decimal. \( \int\left(8-7 x^{4}+\frac{3}{x^{16}}+18 \sqrt{x^{7}}\right) d x \)

Calculate the integral \( \int(8-7x^{4}+\frac{3}{x^{16}}+18\sqrt{x^{7}})dx \). Evaluate the integral by following steps: - step0: Evaluate using partial integration formula: \(\int \left(8-7x^{4}+\frac{3}{x^{16}}+18\sqrt{x^{7}}\right) dx\) - step1: Simplify the root: \(\int \left(8-7x^{4}+\frac{3}{x^{16}}+18x^{3}\sqrt{x}\right) dx\) - step2: Use properties of integrals: \(\int 8 dx+\int -7x^{4} dx+\int \frac{3}{x^{16}} dx+\int 18x^{3}\sqrt{x} dx\) - step3: Evaluate the integral: \(8x+\int -7x^{4} dx+\int \frac{3}{x^{16}} dx+\int 18x^{3}\sqrt{x} dx\) - step4: Evaluate the integral: \(8x-\frac{7x^{5}}{5}+\int \frac{3}{x^{16}} dx+\int 18x^{3}\sqrt{x} dx\) - step5: Evaluate the integral: \(8x-\frac{7x^{5}}{5}-\frac{1}{5x^{15}}+\int 18x^{3}\sqrt{x} dx\) - step6: Evaluate the integral: \(8x-\frac{7x^{5}}{5}-\frac{1}{5x^{15}}+12x^{\frac{9}{2}}-8x^{\frac{9}{2}}\) - step7: Calculate: \(8x-\frac{7x^{5}}{5}-\frac{1}{5x^{15}}+4x^{\frac{9}{2}}\) - step8: Simplify: \(8x-\frac{7x^{5}}{5}-\frac{1}{5x^{15}}+4x^{4}\sqrt{x}\) - step9: Add the constant of integral C: \(8x-\frac{7x^{5}}{5}-\frac{1}{5x^{15}}+4x^{4}\sqrt{x} + C, C \in \mathbb{R}\) The integral of the given function is \(8x - \frac{7x^{5}}{5} - \frac{1}{5x^{15}} + 4x^{4}\sqrt{x} + C\), where \(C\) is an arbitrary constant.