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

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

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integral of (4x^3+3sin(x)+sec(x)tan(x))

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

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

Solution steps

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

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

\int 3 sin (x) d x = - 3 cos (x)

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

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

Add a constant to the solution

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

\int (1 + u + u^{2} + u^{3}) d u

\int \frac{1}{1 - x ^{2}} d (1 - x^{2}) d x

\int 2 e^{t} - 3 cos (t) d t

\int x (3 x^{2} + 1)^{4} d x

\int (\frac{1}{x} + \frac{1}{x ln ( x )}) d x

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