What is the integral of ysec^2(m)y ?

The integral of ysec^2(m)y is (y^3sec^2(m))/3+C

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integral of ysec^2(m)y

\int y sec^{2} (m) y d y

\frac{y ^{3} sec ^{2} ( m )}{3} + C

Solution steps

\int y sec^{2} (m) y d y

Take the constant out:

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

= sec^{2} (m) \cdot \int yy d y

Simplify

yy : y^{2}

= sec^{2} (m) \cdot \int y^{2} d y

Apply the Power Rule

= sec^{2} (m) \frac{y ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{y ^{3} sec ^{2} ( m )}{3}

Add a constant to the solution

= \frac{y ^{3} sec ^{2} ( m )}{3} + C

What is the integral of ysec^2(m)y ?
The integral of ysec^2(m)y is (y^3sec^2(m))/3+C