Question

(1²+x²+2x)(1³+x³+2x+2x²)​

Answer 1

Answer:

ANSWER

∫

x

3

2x

4

−2x

2

+1

x

2

−1

dx

⇒ ∫

x

5

x

3

2x

4

−2x

2

+1

x

5

x

2

−1

dx

⇒ ∫

x

2

2x

4

−2x

2

+1

x

3

1

−

x

5

1

dx

⇒ ∫

2−

x

2

2

+

x

4

1

x

3

1

−

x

5

1

dx

Let 2−

x

2

2

+

x

4

1

=t

(0+

x

3

4

−

x

5

4

)dx=dt

(

x

3

1

−

x

5

1

)=

4

dt

Now, substituting above value,

⇒ ∫

4

t

dt

⇒

4

1

∫t

2

−1

dt

⇒

4

1

2

−1

+1

t

2

−1

+1

+c

⇒

4

1

2

1

t

2

1

+c

⇒

2

t

+c

⇒

2

2−

x

2

2

+

x

4

1

+c

⇒

2x

2

2x

4

−2x

2

+1

Answer 2

Answer:

$(x+1)^{3}(x^{2}+x+1)$ or $x^{5} +4x^{4}+7x^{3}+7x^{2}+4x+1$

Step-by-step explanation:

Solution 1:

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

Solution 2:

$(1+x^{2}+2x)(1+x^{3}+2x^{2}+2x)\\(x^{2} +2x+1)(x^{3}+2x^{2} +2x+1)\\x^{5}+x^{2} (2x^{2})+x^{2}(2x)+x^{2} (1)+2xx^{3}+2x(2x^{2} )+(2x)^{2}+2x(1)+1x^{3}+1(2x^{2})+1(2x)+1\\x^{4}(2)+x^{5}+2x^{4}+x^{3}+4x^{3}+x^{3}(2)+2x^{2}+x^{2} +2^{2}(x^{2})+2x+2x+1\\4x^{2}+x^{5}+2x^{4}+2x^{4}+7x^{3}+3x^{2}+4x+1\\x^{5}+4x^{4}+7x^{3}+7x^{2}+4x+1$