What is the integral of sec^2(10x+7) ?

The integral of sec^2(10x+7) is -7/10+1/10 tan(10x+7)+C

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integral of sec^2(10x+7)

\int sec^{2} (10 x + 7) d x

- \frac{7}{10} + \frac{1}{10} tan (10 x + 7) + C

Solution steps

\int sec^{2} (10 x + 7) d x

Rewrite using trig identities

= \int 1 + tan^{2} (10 x + 7) 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 1 d x + \int tan^{2} (10 x + 7) d x

\int 1 d x = x

\int tan^{2} (10 x + 7) d x = - x - \frac{7}{10} + \frac{1}{10} tan (10 x + 7)

= x - x - \frac{7}{10} + \frac{1}{10} tan (10 x + 7)

Simplify

= - \frac{7}{10} + \frac{1}{10} tan (10 x + 7)

Add a constant to the solution

= - \frac{7}{10} + \frac{1}{10} tan (10 x + 7) + C

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What is the integral of sec^2(10x+7) ?
The integral of sec^2(10x+7) is -7/10+1/10 tan(10x+7)+C