What is the integral of 7(1+tan^2(x)) ?

The integral of 7(1+tan^2(x)) is 7tan(x)+C

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integral of 7(1+tan^2(x))

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

7 tan (x) + C

Solution steps

\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} (e^{- a x})

\int \frac{56}{1 - cos ( 7 x )} d x

\frac{d}{d x} (\frac{3 x ^{2} + 3}{x})

\int \frac{t ^{3}}{4 3 + t ^{4}} d t

\int_{0}^{1} e^{- s t} (t) d t

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