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

The integral of 7+7tan^2(x) is 7tan(x)+C

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integral of 7+7tan^2(x)

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

7 tan (x) + C

Solution steps

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

7 + 7 tan^{2} (x) = 7 (1 + tan^{2} (x))

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

Take the constant out:

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

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

Rewrite using trig identities

= 7 \cdot \int sec^{2} (x) d x

Use the common integral:

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

= 7 tan (x)

Add a constant to the solution

= 7 tan (x) + C

\frac{d}{d x} (\frac{3 cos ( x )}{1 - sin ( x )})

\int \frac{x ^{3} - x ^{2} + 2}{x ^{3} - 2 x ^{2} + 2 x} d x

\int_{5}^{10} \frac{8}{5 - 2 x} d x

y = \frac{1}{3} (x^{2} + 2)^{\frac{3}{2}}

sec (9 x)