Question

integral cosh (2x+1)​

Answer 1

Answer:

$\int\limits {cos(2x+1)} \, dx$ = $\frac{1}{2} sin (2x+1)$

Step-by-step explanation:

integral cos (2x+1)​

We will do this by substitution method

$\int\limits {cos(2x+1)} \, dx$ -------- Equation 1

Let us substitute u = 2x + 1 ----------- Equation 2

now differentiate both side with respect to x

$\frac{d(u)}{dx} = \frac{d(2x+1)}{dx}$

$\frac{du}{dx} = \frac{d(2x)}{dx} + \frac{d(1)}{dx}$

    = 2 + 0                         {differentiation of any constants like 1,2,3,4 .... is 0}

$\frac{du}{dx}$ = 2

dx =  $\frac{du}{2}$ ----------- Equation 2

Now substituting equation 2 and 3 in equation 1 we get;

$\int\limits {cos(2x+1)} \, dx$  = $\int\limits{cos (u)} \, \frac{du}{2}$         {Now it is simple right}

                           = $\frac{1}{2} \int\limits {cosu} \, du$       {$\frac{1}{2}$ is constant so we took it out}

                            = $\frac{1}{2} sinu$              {integration of cos x is sin x}

Now substitute the value of u from equation 1

$\int\limits {cos(2x+1)} \, dx$ = $\frac{1}{2} sin (2x+1)$

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