What is the integral of (1/2 sec^2(x)+x) ?

The integral of (1/2 sec^2(x)+x) is 1/2 tan(x)+(x^2)/2+C

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integral of (1/2 sec^2(x)+x)

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

\frac{1}{2} tan (x) + \frac{x ^{2}}{2} + C

Solution steps

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

\int \frac{1}{2} sec^{2} (x) d x = \frac{1}{2} tan (x)

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

= \frac{1}{2} tan (x) + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{1}{2} tan (x) + \frac{x ^{2}}{2} + C

What is the integral of (1/2 sec^2(x)+x) ?
The integral of (1/2 sec^2(x)+x) is 1/2 tan(x)+(x^2)/2+C