What is the integral of 3sec^2(x)tan(x) ?

The integral of 3sec^2(x)tan(x) is 3/2 tan^2(x)+C

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integral of 3sec^2(x)tan(x)

\int 3 sec^{2} (x) tan (x) d x

\frac{3}{2} tan^{2} (x) + C

Solution steps

\int 3 sec^{2} (x) tan (x) d x

Take the constant out:

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

= 3 \cdot \int sec^{2} (x) tan (x) d x

Apply u-substitution

: \int u d u

= 3 \cdot \int u d u

Apply the Power Rule

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

= 3 \cdot \frac{u ^{2}}{2}

Substitute back

u = tan (x)

= 3 \cdot \frac{tan ^{2} ( x )}{2}

Simplify

3 \cdot \frac{tan ^{2} ( x )}{2} : \frac{3}{2} tan^{2} (x)

= \frac{3}{2} tan^{2} (x)

Add a constant to the solution

= \frac{3}{2} tan^{2} (x) + C

x \to 3 lim (I n (x^{2} - 9))

\int e^{a x} sin (b) x d x

\frac{\partial}{\partial y} (y arcsin (x y))

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

\frac{x}{x + 5}

What is the integral of 3sec^2(x)tan(x) ?
The integral of 3sec^2(x)tan(x) is 3/2 tan^2(x)+C