What is the integral of 3x^{4/3}-sin(x)+c ?

The integral of 3x^{4/3}-sin(x)+c is 9/7 x^{7/3}+cos(x)+cx+C

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integral of 3x^{4/3}-sin(x)+c

\int 3 x^{\frac{4}{3}} - sin (x) + c d x

\frac{9}{7} x^{\frac{7}{3}} + cos (x) + c x + C

Solution steps

\int 3 x^{\frac{4}{3}} - sin (x) + c 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^{\frac{4}{3}} d x - \int sin (x) d x + \int c d x

\int 3 x^{\frac{4}{3}} d x = \frac{9}{7} x^{\frac{7}{3}}

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

\int c d x = c x

= \frac{9}{7} x^{\frac{7}{3}} - (- cos (x)) + c x

Simplify

= \frac{9}{7} x^{\frac{7}{3}} + cos (x) + c x

Add a constant to the solution

= \frac{9}{7} x^{\frac{7}{3}} + cos (x) + c x + C

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{6}})

\int \frac{1}{( x + 2 ) ( x + 3 )} d x

\int \frac{5 x ^{2} + 3 x - 2}{x ^{3} + 2 x ^{2}} d x

x \to 0 lim (\frac{4 x}{x})

3 t \cdot cos (2 t)

What is the integral of 3x^{4/3}-sin(x)+c ?
The integral of 3x^{4/3}-sin(x)+c is 9/7 x^{7/3}+cos(x)+cx+C