What is the integral of tan(x)+x^6+e^x ?

The integral of tan(x)+x^6+e^x is -ln|cos(x)|+(x^7)/7+e^x+C

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integral of tan(x)+x^6+e^x

integral

tan (x) + x^{6} + e^{x}

- ln ∣ cos (x) ∣ + \frac{x ^{7}}{7} + e^{x} + C

Solution steps

\int tan (x) + x^{6} + e^{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 tan (x) d x + \int x^{6} d x + \int e^{x} d x

\int tan (x) d x = - ln ∣ cos (x) ∣

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

\int e^{x} d x = e^{x}

= - ln ∣ cos (x) ∣ + \frac{x ^{7}}{7} + e^{x}

Add a constant to the solution

= - ln ∣ cos (x) ∣ + \frac{x ^{7}}{7} + e^{x} + C

\frac{1}{( 3 x ^{2} )}

\frac{( x ^{5} - 1 )}{x - 1}

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

3 x^{7}

\frac{( x ^{3} + 4 )}{x}

What is the integral of tan(x)+x^6+e^x ?
The integral of tan(x)+x^6+e^x is -ln|cos(x)|+(x^7)/7+e^x+C