What is the integral of 12x^3+sec(x)tan(x) ?

The integral of 12x^3+sec(x)tan(x) is 3x^4+sec(x)+C

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integral of 12x^3+sec(x)tan(x)

\int 12 x^{3} + sec (x) tan (x) d x

3 x^{4} + sec (x) + C

Solution steps

\int 12 x^{3} + sec (x) tan (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 12 x^{3} d x + \int sec (x) tan (x) d x

\int 12 x^{3} d x = 3 x^{4}

\int sec (x) tan (x) d x = sec (x)

= 3 x^{4} + sec (x)

Add a constant to the solution

= 3 x^{4} + sec (x) + C

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What is the integral of 12x^3+sec(x)tan(x) ?
The integral of 12x^3+sec(x)tan(x) is 3x^4+sec(x)+C