What is the integral of 7xsec(x)tan(x) ?

The integral of 7xsec(x)tan(x) is 7(xsec(x)-ln|tan(x)+sec(x)|)+C

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integral of 7xsec(x)tan(x)

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

7 (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: x sec (x) - \int sec (x) d x

= 7 (x sec (x) - \int sec (x) d x)

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= 7 (x sec (x) - ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= 7 (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

\int \frac{1}{( 576 + x ^{2} ) ^{\frac{3}{2}}} d x

\int 2 a cos (\frac{θ}{2}) d θ

\frac{d}{d x} (\frac{1}{2} x + 2)

(1 + cos^{2} (x))^{6}

t \to π lim (- 2 sin (- \frac{t}{2}))

What is the integral of 7xsec(x)tan(x) ?
The integral of 7xsec(x)tan(x) is 7(xsec(x)-ln|tan(x)+sec(x)|)+C