What is the integral of 3sqrt(x)-(sin(x))/(cos^2(x)) ?

The integral of 3sqrt(x)-(sin(x))/(cos^2(x)) is 2x^{3/2}-sec(x)+C

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integral of 3sqrt(x)-(sin(x))/(cos^2(x))

\int 3 x - \frac{sin ( x )}{cos ^{2} ( x )} d x

2 x^{\frac{3}{2}} - sec (x) + C

Solution steps

\int 3 x - \frac{sin ( x )}{cos ^{2} ( x )} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 x d x - \int \frac{sin ( x )}{cos ^{2} ( x )} d x

\int 3 x d x = 2 x^{\frac{3}{2}}

\int \frac{sin ( x )}{cos ^{2} ( x )} d x = sec (x)

= 2 x^{\frac{3}{2}} - sec (x)

Add a constant to the solution

= 2 x^{\frac{3}{2}} - sec (x) + C

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What is the integral of 3sqrt(x)-(sin(x))/(cos^2(x)) ?
The integral of 3sqrt(x)-(sin(x))/(cos^2(x)) is 2x^{3/2}-sec(x)+C