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

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

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integral of tan^2(x)*sec^2(x)

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

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

Solution steps

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

Rewrite using trig identities

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

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

Add a constant to the solution

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

\frac{d}{d x} ((x^{3} + 3) e^{x})

\frac{\partial}{\partial x} (A x + B y + C e^{x y})

\int_{0}^{5} \frac{1}{x ^{\frac{5}{2}}} d x

\int 3 x^{2} - 4 x + 1 d x

f (x) = (x^{2} + x + 1)^{3}

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