What is the integral of-sec^3(x)sin(x) ?

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

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integral of-sec^3(x)sin(x)

\int - sec^{3} (x) sin (x) d x

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

Solution steps

\int - sec^{3} (x) sin (x) d x

Take the constant out:

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

= - \int sec^{3} (x) sin (x) d x

Rewrite using trig identities

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

Apply u-substitution

: \int u d u

= - \int u d u

Apply the Power Rule

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

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

Substitute back

u = tan (x)

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

Add a constant to the solution

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

\int_{7}^{e^{4}} \frac{1}{x} d x

7 x - x^{2}, 2 x, 0, 5

\frac{2 t}{t ^{2} + 1}

\int ∣ x + 2 ∣ d x

\frac{d}{d x} ((5 x^{2} - 3) \cdot (x^{2} + x + 4))

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