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Find $\int \cos(4x+1) \,dx$. - Scottish Highers Maths - Question 5 - 2016

Question 5

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Find $\int \cos(4x+1) \,dx$.

Worked Solution & Example Answer:Find $\int \cos(4x+1) \,dx$. - Scottish Highers Maths - Question 5 - 2016

Step 1

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Answer

To find the integral of the function, we can start by using a substitution. Let's set:

$u = 4x + 1$

Then, the differential is:

$du = 4 \,dx \, \Rightarrow \, dx = \frac{du}{4}$

Now we can rewrite the integral in terms of $u$ .

Step 2

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Answer

Substituting into the integral, we get:

$\int \cos(4x + 1) \,dx = \int \cos(u) \cdot \frac{du}{4}$

This simplifies to:

$\frac{1}{4} \int \cos(u) \,du = \frac{1}{4} \sin(u) + C$

Finally, substituting back for $u$ :

$\frac{1}{4} \sin(4x + 1) + C$

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