What is the integral of (sec^2(x)+x) ?

The integral of (sec^2(x)+x) is tan(x)+(x^2)/2+C

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integral of (sec^2(x)+x)

\int (sec^{2} (x) + x) d x

tan (x) + \frac{x ^{2}}{2} + C

Solution steps

\int sec^{2} (x) + 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 sec^{2} (x) d x + \int x d x

\int sec^{2} (x) d x = tan (x)

\int x d x = \frac{x ^{2}}{2}

= tan (x) + \frac{x ^{2}}{2}

Add a constant to the solution

= tan (x) + \frac{x ^{2}}{2} + C

\int_{b}^{a} f (x) d x

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x \to 0 lim (e^{x^{2}})

\int_{1}^{2} x^{3} ln (x) d x

\int 2 sin (x) + 1 d x

What is the integral of (sec^2(x)+x) ?
The integral of (sec^2(x)+x) is tan(x)+(x^2)/2+C