Question

integrate 3x² (4x⁴ + 5)⅗ dx​

Answer 1

$\bold\red{10x-\frac{3{x}^{2}}{2}-\frac{19 {x}^{3} }{3} + 3 {x}^{4} + c}$

Step-by-step explanation:

Given,

$\begin{gathered}\sf\int(1 - x)(2 + 3x)(5 - 4x)dx \\ \\\sf =\int(10 - 3x - 19 {x}^{2} + 12 {x}^{3} )dx \\ \\ \sf= 10\int \: dx - 3\int \: xdx - 19\int {x}^{2} dx + 12\int {x}^{3} dx \\ \\ \sf= 10x - 3 \times \frac{ {x}^{2} }{2} - 19 \times \frac{ {x}^{3} }{3} + 12 \times \frac{ {x}^{4} }{4} + c \\ \\\sf = 10x - \frac{3 {x}^{2} }{2} - \frac{19 {x}^{3} }{3} + 3 {x}^{4} + c\end{gathered}$

• Hence,

$\tt Values = \bold{10x-\frac{3{x}^{2}}{2}-\frac{19 {x}^{3} }{3} + 3 {x}^{4} + c}$