Question

Intigeration 3x²+7x​

Answer 1

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Integrate

$\sf\int\:3x^2+7x\:dx$

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We have to integrate :

$\sf\int\:3x^2+7x\:dx$

$\sf\int\:3x^2\:dx+\int7x\:dx$

We know that

$\sf\int\:x^n=\dfrac{x^{n+1}}{n+1}$

Then ,

$\sf\int\:3x^2\:dx+\int7x\:dx$

$\sf=3\times\dfrac{3x^{2+1}}{2+1}+7\times\dfrac{x^{1+1}}{1+1}+c$

$\sf=3\times\dfrac{3x^{3}}{3}+7\times\dfrac{x^{2}}{2}+c$

$\sf=\dfrac{9x^{3}}{3}+\dfrac{7x^{2}}{2}+c$

$\sf=3x^3+\dfrac{7x^2}{2}+c$

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Answer 2

Answer:

We have to integrate :

\sf\int\:3x^2+7x\:dx∫3x

2

+7xdx

\sf\int\:3x^2\:dx+\int7x\:dx∫3x

2

dx+∫7xdx

We know that

\sf\int\:x^n=\dfrac{x^{n+1}}{n+1}∫x

n

=

n+1

x

n+1

Then ,

\sf\int\:3x^2\:dx+\int7x\:dx∫3x

2

dx+∫7xdx

\sf=3\times\dfrac{3x^{2+1}}{2+1}+7\times\dfrac{x^{1+1}}{1+1}+c=3×

2+1

3x

2+1

+7×

1+1

x

1+1

+c

\sf=3\times\dfrac{3x^{3}}{3}+7\times\dfrac{x^{2}}{2}+c=3×

3

3x

3

+7×

2

x

2

+c

\sf=\dfrac{9x^{3}}{3}+\dfrac{7x^{2}}{2}+c=

3

9x

3

+

2

7x

2

+c

\sf=3x^3+\dfrac{7x^2}{2}+c=3x

3

+

2

7x

2

+c