What is the integral of 4/15 x^{5/2}+9cos(x)+Cx+C ?

The integral of 4/15 x^{5/2}+9cos(x)+Cx+C is 8/105 x^{7/2}+9sin(x)+(Cx^2)/2+Cx+C

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integral of 4/15 x^{5/2}+9cos(x)+Cx+C

\int \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C x + C d x

\frac{8}{105} x^{\frac{7}{2}} + 9 sin (x) + \frac{C x ^{2}}{2} + C x + C

Solution steps

\int \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C 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 \frac{4}{15} x^{\frac{5}{2}} d x + \int 9 cos (x) d x + \int C x d x + \int C d x

\int \frac{4}{15} x^{\frac{5}{2}} d x = \frac{8}{105} x^{\frac{7}{2}}

\int 9 cos (x) d x = 9 sin (x)

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

\int C d x = C x

= \frac{8}{105} x^{\frac{7}{2}} + 9 sin (x) + \frac{C x ^{2}}{2} + C x

Add a constant to the solution

= \frac{8}{105} x^{\frac{7}{2}} + 9 sin (x) + \frac{C x ^{2}}{2} + C x + C

\int \frac{1}{x ^{2}} + \frac{1}{x} d x

x \to \frac{π}{2} lim (9 tan (x))

\frac{d}{d x} (ln (ln (6 x)))

\int e^{t (1 - s)} d t

\int_{0}^{\frac{π}{2}} - 6 cos^{5} (x) d x

What is the integral of 4/15 x^{5/2}+9cos(x)+Cx+C ?
The integral of 4/15 x^{5/2}+9cos(x)+Cx+C is 8/105 x^{7/2}+9sin(x)+(Cx^2)/2+Cx+C