What is the integral of 8tan(x)sec^5(x) ?

The integral of 8tan(x)sec^5(x) is 8/5 sec^5(x)+C

Popular >

integral of 8tan(x)sec^5(x)

\int 8 tan (x) sec^{5} (x) d x

\frac{8}{5} sec^{5} (x) + C

Solution steps

\int 8 tan (x) sec^{5} (x) d x

Take the constant out:

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

= 8 \cdot \int tan (x) sec^{5} (x) d x

Apply u-substitution

: \int u^{4} d u

= 8 \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 8 \cdot \frac{u ^{5}}{5}

Substitute back

u = sec (x)

= 8 \cdot \frac{sec ^{5} ( x )}{5}

Simplify

8 \cdot \frac{sec ^{5} ( x )}{5} : \frac{8}{5} sec^{5} (x)

= \frac{8}{5} sec^{5} (x)

Add a constant to the solution

= \frac{8}{5} sec^{5} (x) + C

\int \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{t ^{6}} d t

\int x^{2} \frac{d ^{2} y}{1} d x^{2}

\int e^{x} (1 + tan (e^{x})) d x

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

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

What is the integral of 8tan(x)sec^5(x) ?
The integral of 8tan(x)sec^5(x) is 8/5 sec^5(x)+C