What is the integral of 3x^2+5x^{1/3}+7sin(x) ?

The integral of 3x^2+5x^{1/3}+7sin(x) is x^3+15/4 x^{4/3}-7cos(x)+C

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integral of 3x^2+5x^{1/3}+7sin(x)

\int 3 x^{2} + 5 x^{\frac{1}{3}} + 7 sin (x) d x

x^{3} + \frac{15}{4} x^{\frac{4}{3}} - 7 cos (x) + C

Solution steps

\int 3 x^{2} + 5 x^{\frac{1}{3}} + 7 sin (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 3 x^{2} d x + \int 5 x^{\frac{1}{3}} d x + \int 7 sin (x) d x

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

\int 5 x^{\frac{1}{3}} d x = \frac{15}{4} x^{\frac{4}{3}}

\int 7 sin (x) d x = - 7 cos (x)

= x^{3} + \frac{15}{4} x^{\frac{4}{3}} - 7 cos (x)

Add a constant to the solution

= x^{3} + \frac{15}{4} x^{\frac{4}{3}} - 7 cos (x) + C

sin (x), cos (x), [0, π]

y = 7 x^{3} - x^{e}

\frac{d y}{d x} = \frac{x}{2 y}

y = \frac{1}{4 x ^{3}} - \frac{6}{5 x ^{4}}

F (s) = ln (ln (3 s))

What is the integral of 3x^2+5x^{1/3}+7sin(x) ?
The integral of 3x^2+5x^{1/3}+7sin(x) is x^3+15/4 x^{4/3}-7cos(x)+C