What is the integral of 6tan^4(x) ?

The integral of 6tan^4(x) is 6(1/3 tan^3(x)+x-tan(x))+C

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integral of 6tan^4(x)

\int 6 tan^{4} (x) d x

6 (\frac{1}{3} tan^{3} (x) + x - tan (x)) + C

Solution steps

\int 6 tan^{4} (x) d x

Take the constant out:

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

= 6 \cdot \int tan^{4} (x) d x

Apply Integral Reduction

= 6 (\frac{tan ^{3} ( x )}{3} - \int tan^{2} (x) d x)

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

= 6 (\frac{tan ^{3} ( x )}{3} - (- x + tan (x)))

Simplify

6 (\frac{tan ^{3} ( x )}{3} - (- x + tan (x))) : 6 (\frac{1}{3} tan^{3} (x) + x - tan (x))

= 6 (\frac{1}{3} tan^{3} (x) + x - tan (x))

Add a constant to the solution

= 6 (\frac{1}{3} tan^{3} (x) + x - tan (x)) + C

\frac{\partial}{\partial x} (2 x + y + 1)

\int \frac{3 x ^{2} - 7}{x ^{3} - 7 x + 6} d x

\int_{0}^{1} (t 4 + 9 t^{2}) d t

x + 2 y = x + 2 y = 8

y^{^{'}} = 5 x (x - 3)

What is the integral of 6tan^4(x) ?
The integral of 6tan^4(x) is 6(1/3 tan^3(x)+x-tan(x))+C