What is the integral of (5x^2-5x+4tan(x)) ?

The integral of (5x^2-5x+4tan(x)) is (5x^3)/3-(5x^2)/2-4ln|cos(x)|+C

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integral of (5x^2-5x+4tan(x))

\int (5 x^{2} - 5 x + 4 tan (x)) d x

\frac{5 x ^{3}}{3} - \frac{5 x ^{2}}{2} - 4 ln ∣ cos (x) ∣ + C

Solution steps

\int 5 x^{2} - 5 x + 4 tan (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 5 x^{2} d x - \int 5 x d x + \int 4 tan (x) d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 4 tan (x) d x = - 4 ln ∣ cos (x) ∣

= \frac{5 x ^{3}}{3} - \frac{5 x ^{2}}{2} - 4 ln ∣ cos (x) ∣

Add a constant to the solution

= \frac{5 x ^{3}}{3} - \frac{5 x ^{2}}{2} - 4 ln ∣ cos (x) ∣ + C

\frac{d}{d x} (20 x (2 x^{2} + 7)^{4})

2 + 6 x^{2} - 2 x^{3}

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

\frac{\partial}{\partial x} (a x^{2} + b y^{2})

What is the integral of (5x^2-5x+4tan(x)) ?
The integral of (5x^2-5x+4tan(x)) is (5x^3)/3-(5x^2)/2-4ln|cos(x)|+C