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

The integral of (1+cos^2(x)) is 3/2 x+1/4 sin(2x)+C

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integral of (1+cos^2(x))

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

\frac{3}{2} x + \frac{1}{4} sin (2 x) + C

Solution steps

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

\int 1 d x = x

\int cos^{2} (x) d x = \frac{1}{2} (x + \frac{1}{2} sin (2 x))

= x + \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Simplify

x + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) : \frac{3}{2} x + \frac{1}{4} sin (2 x)

= \frac{3}{2} x + \frac{1}{4} sin (2 x)

Add a constant to the solution

= \frac{3}{2} x + \frac{1}{4} sin (2 x) + C

n = 1 \sum \infty \frac{7 ^{n}}{6 ^{n}}

x \to \infty lim (5 e^{- t} i - \frac{5 t}{t + 7} j + 5 arctan (t k))

y^{^{'}} = - 6 y

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 5 x)

x^{2} y^{^{'}} + (2 - y) = 0

What is the integral of (1+cos^2(x)) ?
The integral of (1+cos^2(x)) is 3/2 x+1/4 sin(2x)+C