Question

4. S (x3 + 3x2 + 3x+1)dx​

Answer 1

${\bold{\huge{\red{\underline{\green{ANSWER}}}}}}$

$\frac{d}{dx}( {x}^{3} + 3 {x}^{2} + 3x + 1)$

diffrentiate with respect to x

we get,

$3 {x}^{2} + 6x + 3$

hope it help➡❤

Answer 2

Answer:

$\large\boxed{ \sf{\frac{ {x}^{4} }{4} + {x}^{3} + \frac{3}{2} {x}^{2} + x + c}}$

Step-by-step explanation:

We have to integrate :

$\displaystyle\int({x}^{3} + 3 {x}^{2} + 3x + 1)dx$

Integration:

$= \displaystyle\int {x}^{3} dx + 3\displaystyle\int {x}^{2} dx+ 3\displaystyle\int \: x dx + \displaystyle\int \: dx \\ \\ = \frac{ {x}^{(3 + 1)} }{3 + 1} + 3 \times \frac{ {x}^{(2 + 1)} }{2 + 1} + 3 \times \frac{ {x}^{(1 + 1)} }{1 + 1} + \frac{ {x}^{(0 + 1)} }{0 + 1} + c \\ \\ = \frac{ {x}^{4} }{4} + \frac{3 {x}^{3} }{3} + \frac{3 {x}^{2} }{2} + x + c \\ \\ = \sf{\frac{ {x}^{4} }{4} + {x}^{3} + \frac{3}{2} {x}^{2} + x + c}$

Here, c is the integral constant.

Concept Map:-

• $\displaystyle\int {x}^{n} dx = \frac{ {x}^{(n + 1)} }{n + 1} + c$