What is the integral of 3sec^2(x)cos(4+tan(x)) ?

The integral of 3sec^2(x)cos(4+tan(x)) is 3sin(4+tan(x))+C

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integral of 3sec^2(x)cos(4+tan(x))

\int 3 sec^{2} (x) cos (4 + tan (x)) d x

3 sin (4 + tan (x)) + C

Solution steps

\int 3 sec^{2} (x) cos (4 + tan (x)) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int sec^{2} (x) cos (4 + tan (x)) d x

Apply u-substitution

: \int cos (4 + u) d u

= 3 \cdot \int cos (4 + u) d u

Apply u-substitution

: \int cos (v) d v

= 3 \cdot \int cos (v) d v

Use the common integral:

\int cos (v) d v = sin (v)

= 3 sin (v)

Substitute back

= 3 sin (4 + tan (x))

Add a constant to the solution

= 3 sin (4 + tan (x)) + C

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What is the integral of 3sec^2(x)cos(4+tan(x)) ?
The integral of 3sec^2(x)cos(4+tan(x)) is 3sin(4+tan(x))+C