Solve ∫ (3y^4-2y^2+8y-16)*(6y^4+5y^2+10y)

$$\int ( 3 y ^ { 4 } - 2 y ^ { 2 } + 8 y - 16 ) \cdot ( 6 y ^ { 4 } + 5 y ^ { 2 } + 10 y )$$

Evaluate

$$xy\left(6y^{3}+5y+10\right)\left(3y^{4}-2y^{2}+8y-16\right)+С$$

Solution Steps

Find the integral of \left(3y^{4}-2y^{2}+8y-16\right)\left(6y^{4}+5y^{2}+10y\right) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(3y^{4}-2y^{2}+8y-16\right)\left(6y^{4}+5y^{2}+10y\right)x$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\left(3y^{4}-2y^{2}+8y-16\right)\left(6y^{4}+5y^{2}+10y\right)x+С$$

Differentiate w.r.t. x

$$y\left(6y^{3}+5y+10\right)\left(3y^{4}-2y^{2}+8y-16\right)$$