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

hrostentsp6

hrostentsp6

Answered question

2021-11-21

Find the indefinite integral cosh4xdx

Answer & Explanation

Cherry McCormick

Cherry McCormick

Beginner2021-11-22Added 23 answers

Step 1
To find the indefinite integral.
Step 2
Given information:
cosh(4x)dx
Formula used:
cosh(nv)dv=sinh(nv)n+C
Step 3
Calculation:
cosh(4x)dx
From formula,
cosh(4x)dx=sinh(4x)4+C
This is the indefinite integral.
Stephanie Mann

Stephanie Mann

Beginner2021-11-23Added 25 answers

Step 1: Regroup terms.
hcos4xdx
Step 2: Use Constant Factor Rule: cf(x)dx=cf(x)dx.
hcos4xdx
Step 3: Use Integration by Substitution on cos4xdx.
Let u=4x, du=4 dx, then dx=14du
Step 4: Using u and du above, rewrite cos4xdx.
cosu4du
Step 5: Use Constant Factor Rule: cf(x)dx=cf(x)dx.
14cosudu
Step 6: Use Trigonometric Integration: the integral of cosu is sinu.
sinu4
Step 7: Substitute u=4x back into the original integral.
sin4x4
Step 8: Rewrite the integral with the completed substitution.
hsin4x4
Step 9: Add constant.
hsin4x4+C

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