What is the integral of sec^4(x)cos^3(x) ?

The integral of sec^4(x)cos^3(x) is ln|tan(x)+sec(x)|+C

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integral of sec^4(x)cos^3(x)

\int sec^{4} (x) cos^{3} (x) d x

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int sec^{4} (x) cos^{3} (x) d x

Rewrite using trig identities

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

Rewrite using trig identities

= \int sec (x) d x

Use the common integral:

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

= ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ + C

\int \frac{3 x}{2 x ^{2} - 6} d x

\int \frac{1}{3 x + 5} d x

\int \frac{1}{( 3 x + 4 ) ^{3}} d x

\int x^{2} + 121 d x

\int x^{4} (x - 2) (x + 3) d x

What is the integral of sec^4(x)cos^3(x) ?
The integral of sec^4(x)cos^3(x) is ln|tan(x)+sec(x)|+C