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

The integral of (1+tan(x))^2sec^2(x) is ((1+tan(x))^3)/3+C

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

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

\frac{( 1 + tan ( x ) ) ^{3}}{3} + C

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = 1 + tan (x)

= \frac{( 1 + tan ( x ) ) ^{3}}{3}

Add a constant to the solution

= \frac{( 1 + tan ( x ) ) ^{3}}{3} + C

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What is the integral of (1+tan(x))^2sec^2(x) ?
The integral of (1+tan(x))^2sec^2(x) is ((1+tan(x))^3)/3+C