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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int 2 u d u

= \int 2 u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 2 \cdot \frac{u ^{2}}{2}

Substitute back

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

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

Simplify

2 \cdot \frac{( 2 + tan ( \frac{x}{2} ) ) ^{2}}{2} : (2 + tan (\frac{x}{2}))^{2}

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

Add a constant to the solution

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

f (x) = \frac{x}{x ^{2} - 3}

\frac{d}{d x} (e^{0.0211 x})

x \to 2 + lim (2 x^{2} - 6)

\int 20 x^{3} + 12 x^{2} + 8 d x

2 x^{2} - 5 x

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