What is the integral of (sin^4(x))/(cos^6(x)) ?

The integral of (sin^4(x))/(cos^6(x)) is (tan^5(x))/5+C

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integral of (sin^4(x))/(cos^6(x))

\int \frac{sin ^{4} ( x )}{cos ^{6} ( x )} d x

\frac{tan ^{5} ( x )}{5} + C

Solution steps

\int \frac{sin ^{4} ( x )}{cos ^{6} ( x )} d x

Rewrite using trig identities

= \int \frac{tan ^{4} ( x )}{cos ^{2} ( x )} d x

Use the basic trigonometric identity:

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

= \int tan^{4} (x) sec^{2} (x) d x

Rewrite using trig identities

= \int (1 + tan^{2} (x)) tan^{4} (x) d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

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

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

Substitute back

u = tan (x)

= \frac{tan ^{5} ( x )}{5}

Add a constant to the solution

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

f (x) = 7 x, at x = 4

n = 5 \sum \infty \frac{n ^{3}}{2 ^{n}}

f^{^{''}} (x) = 2

x \to - \infty lim (x + \frac{1}{x})

\int_{0}^{\frac{π}{4}} sec (x) d x

What is the integral of (sin^4(x))/(cos^6(x)) ?
The integral of (sin^4(x))/(cos^6(x)) is (tan^5(x))/5+C