What is the integral of tan(10x)sec^2(10x) ?

The integral of tan(10x)sec^2(10x) is 1/20 tan^2(10x)+C

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integral of tan(10x)sec^2(10x)

\int tan (10 x) sec^{2} (10 x) d x

\frac{1}{20} tan^{2} (10 x) + C

Solution steps

\int tan (10 x) sec^{2} (10 x) d x

Apply u-substitution

= \int \frac{u}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int u d u

Apply the Power Rule

= \frac{1}{10} \cdot \frac{u ^{2}}{2}

Substitute back

u = tan (10 x)

= \frac{1}{10} \cdot \frac{tan ^{2} ( 10 x )}{2}

Simplify

\frac{1}{10} \cdot \frac{tan ^{2} ( 10 x )}{2} : \frac{1}{20} tan^{2} (10 x)

= \frac{1}{20} tan^{2} (10 x)

Add a constant to the solution

= \frac{1}{20} tan^{2} (10 x) + C

What is the integral of tan(10x)sec^2(10x) ?
The integral of tan(10x)sec^2(10x) is 1/20 tan^2(10x)+C