Find the indefinite integral ∫cos⁡h4xdx

Question

Cherry McCormick · Accepted Answer

Step 1
To find the indefinite integral.
Step 2
Given information:

\int \cos h (4 x) d x

Formula used:

\int \cos h (n v) d v = \frac{\sin h (n v)}{n} + C

Step 3
Calculation:

\int \cos h (4 x) d x

From formula,

\int \cos h (4 x) d x = \frac{\sin h (4 x)}{4} + C

This is the indefinite integral.

Stephanie Mann · Accepted Answer

Step 1: Regroup terms.  ∫hcos⁡4xdx  Step 2: Use Constant Factor Rule: ∫cf(x)dx=c∫f(x)dx.  h∫cos⁡4xdx  Step 3: Use Integration by Substitution on ∫cos⁡4xdx.  Let u=4x, du=4 dx, then dx=14du  Step 4: Using u and du above, rewrite ∫cos⁡4xdx.  ∫cos⁡u4du  Step 5: Use Constant Factor Rule: ∫cf(x)dx=c∫f(x)dx.  14∫cos⁡udu  Step 6: Use Trigonometric Integration: the integral of cos⁡u is sin⁡u.  sin⁡u4  Step 7: Substitute u=4x back into the original integral.  sin⁡4x4  Step 8: Rewrite the integral with the completed substitution.  hsin⁡4x4  Step 9: Add constant.  hsin⁡4x4+C

Find the indefinite integral \int \cos h 4x dx

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