What is the integral of (tan^8(x))/(sec^9(x)) ?

The integral of (tan^8(x))/(sec^9(x)) is (sin^9(x))/9+C

Popular >

integral of (tan^8(x))/(sec^9(x))

\int \frac{tan ^{8} ( x )}{sec ^{9} ( x )} d x

\frac{sin ^{9} ( x )}{9} + C

Solution steps

\int \frac{tan ^{8} ( x )}{sec ^{9} ( x )} d x

Use the basic trigonometric identity:

\frac{1}{sec ( x )} = cos (x)

= \int cos^{9} (x) tan^{8} (x) d x

Rewrite using trig identities

= \int sin^{8} (x) cos (x) d x

Apply u-substitution

: \int u^{8} d u

= \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= \frac{u ^{9}}{9}

Substitute back

u = sin (x)

= \frac{sin ^{9} ( x )}{9}

Add a constant to the solution

= \frac{sin ^{9} ( x )}{9} + C

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

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

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

\int - 3 ln (x) d x

\int \frac{24 x ^{2}}{25 - x ^{2}} d x

What is the integral of (tan^8(x))/(sec^9(x)) ?
The integral of (tan^8(x))/(sec^9(x)) is (sin^9(x))/9+C