What is the integral of (9x^2+2x)sec^2(3x^3+x^2) ?

The integral of (9x^2+2x)sec^2(3x^3+x^2) is tan(3x^3+x^2)+C

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integral of (9x^2+2x)sec^2(3x^3+x^2)

\int (9 x^{2} + 2 x) sec^{2} (3 x^{3} + x^{2}) d x

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

Solution steps

\int (9 x^{2} + 2 x) sec^{2} (3 x^{3} + x^{2}) d x

Apply u-substitution

: \int sec^{2} (u) d u

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = 3 x^{3} + x^{2}

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

Add a constant to the solution

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

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What is the integral of (9x^2+2x)sec^2(3x^3+x^2) ?
The integral of (9x^2+2x)sec^2(3x^3+x^2) is tan(3x^3+x^2)+C