What is the integral of sec^2(x)(tan(x)+3) ?

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

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integral of sec^2(x)(tan(x)+3)

\int sec^{2} (x) (tan (x) + 3) d x

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

Solution steps

\int sec^{2} (x) (tan (x) + 3) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = tan (x) + 3

= \frac{( tan ( x ) + 3 ) ^{2}}{2}

Add a constant to the solution

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

sin (arcsin (x) + arccos (x))

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\int (e^{8 x} + e^{- 9 x}) d x

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\int \frac{8 e ^{4 x}}{x} d x

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