Integrate 2x+5 from 1 to 2

\int_{1}^{2}\left(2x+5\right)dx

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ln
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sin
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asin
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sinh
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asinh
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asech
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Answer

$8$

Step by step solution

Problem

$\int_{1}^{2}\left(2x+5\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int_{1}^{2}5dx+\int_{1}^{2}2xdx$
2

The integral of a constant is equal to the constant times the integral's variable

$\left[5x\right]_{1}^{2}+\int_{1}^{2}2xdx$
3

Evaluate the definite integral

$\int_{1}^{2}2xdx-1\cdot 1\cdot 5+2\cdot 5$
4

Multiply $5$ times $2$

$\int_{1}^{2}2xdx-5+10$
5

Subtract the values $10$ and $-5$

$\int_{1}^{2}2xdx+5$
6

Taking the constant out of the integral

$2\int_{1}^{2} xdx+5$
7

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$2\left[\frac{1}{2}x^2\right]_{1}^{2}+5$
8

Evaluate the definite integral

$\left(2^2\cdot 0.5-1\cdot 1^2\cdot 0.5\right)\cdot 2+5$
9

Multiply $\frac{1}{2}$ times $-1$

$\left(1^2\left(-0.5\right)+2^2\cdot 0.5\right)\cdot 2+5$
10

Calculate the power

$\left(1\left(-0.5\right)+4\cdot 0.5\right)\cdot 2+5$
11

Multiply $\frac{1}{2}$ times $4$

$\left(2-0.5\right)\cdot 2+5$
12

Subtract the values $2$ and $-\frac{1}{2}$

$1.5\cdot 2+5$
13

Multiply $2$ times $\frac{3}{2}$

$3+5$
14

Add the values $5$ and $3$

$8$

Answer

$8$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.21 seconds

Views:

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