What is the integral of (1+tan(x))^5sec^2(x) ?

The integral of (1+tan(x))^5sec^2(x) is ((1+tan(x))^6)/6+C

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integral of (1+tan(x))^5sec^2(x)

\int (1 + tan (x))^{5} sec^{2} (x) d x

\frac{( 1 + tan ( x ) ) ^{6}}{6} + C

Solution steps

\int (1 + tan (x))^{5} sec^{2} (x) d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = 1 + tan (x)

= \frac{( 1 + tan ( x ) ) ^{6}}{6}

Add a constant to the solution

= \frac{( 1 + tan ( x ) ) ^{6}}{6} + C

y = 3 cos (2 x)

\int_{1}^{4} (x - 3)^{2} d x

x y^{^{'}} + y = 8 x y^{2}, y (1) = 3

\frac{d}{d x} (cos (2 \cdot x))

y = 8 x, (4, 16)

What is the integral of (1+tan(x))^5sec^2(x) ?
The integral of (1+tan(x))^5sec^2(x) is ((1+tan(x))^6)/6+C