What is the integral of tan(b)x ?

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

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integral of tan(b)x

\int tan (b) x d x

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

Solution steps

\int tan (b) x d x

Take the constant out:

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

= tan (b) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Simplify

tan (b) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} tan (b)

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

Add a constant to the solution

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

f (x) = tan (e^{x})

10 y^{^{''}} - 10 y^{^{'}} + 65 y = 0

x \to - 3 + lim (\frac{2}{x ^{2} - 9})

f (x) = 4 x^{2} + 3

\frac{d}{d x} \frac{( x ^{2} + 5 ) ^{3}}{9} + 3