What is the integral of-7sec(2x)tan(2x) ?

The integral of-7sec(2x)tan(2x) is -7(1/2 cos(2x)+1/2 sin(2x)tan(2x))+C

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integral of-7sec(2x)tan(2x)

\int - 7 sec (2 x) tan (2 x) d x

- 7 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)) + C

Solution steps

\int - 7 sec (2 x) tan (2 x) d x

Take the constant out:

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

= - 7 \cdot \int sec (2 x) tan (2 x) d x

Rewrite using trig identities

= - 7 \cdot \int \frac{sin ( 2 x )}{cos ^{2} ( 2 x )} d x

Apply Integration By Parts

= - 7 (- \int sin (2 x) d x + \frac{1}{2} sin (2 x) tan (2 x))

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

= - 7 (- (- \frac{1}{2} cos (2 x)) + \frac{1}{2} sin (2 x) tan (2 x))

Simplify

= - 7 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x))

Add a constant to the solution

= - 7 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)) + C

\int \frac{3 x}{x ^{2} + 1} d x

\frac{d}{d x} (e^{3 x - 2})

\int cot^{3} (5 x) d x

\int \frac{2 x ^{3} + 7 x ^{2} + 2 x + 9}{2 x + 3} d x

y^{^{'}} - 2 y = - 4 y^{3}

What is the integral of-7sec(2x)tan(2x) ?
The integral of-7sec(2x)tan(2x) is -7(1/2 cos(2x)+1/2 sin(2x)tan(2x))+C