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

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

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integral of 2+tan^2(x)

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

tan (x) + x + C

Solution steps

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

Rewrite using trig identities

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

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

\int 1 d x = x

= tan (x) + x

Add a constant to the solution

= tan (x) + x + C

x \to \infty + lim (6 x)

7 x^{2} y^{^{''}} + 15 x y^{^{'}} + y = 48 x + 7

\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 6

\int sin (2 x) - 4 e^{3 x} d x

n = 2 \sum \infty \frac{1}{n ^{2} + 4 n}