What is the integral of (x^6+sec^2(x)) ?

The integral of (x^6+sec^2(x)) is (x^7)/7+tan(x)+C

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integral of (x^6+sec^2(x))

\int (x^{6} + sec^{2} (x)) d x

\frac{x ^{7}}{7} + tan (x) + C

Solution steps

\int x^{6} + sec^{2} (x) 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 x^{6} d x + \int sec^{2} (x) d x

\int x^{6} d x = \frac{x ^{7}}{7}

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

= \frac{x ^{7}}{7} + tan (x)

Add a constant to the solution

= \frac{x ^{7}}{7} + tan (x) + C

\int \frac{1}{x ( x + 1 )} d x

d er i v a t i v e 3 x^{2 x}

\int \frac{x ^{3} + 1}{x ^{2} + 1} d x

d er i v a t i v e y = \frac{x}{x + 1}

\frac{d}{d x} (x^{2} - m^{2})

What is the integral of (x^6+sec^2(x)) ?
The integral of (x^6+sec^2(x)) is (x^7)/7+tan(x)+C