What is the integral of (x^3+5)^2 ?

The integral of (x^3+5)^2 is (x^7)/7+(5x^4)/2+25x+C

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integral of (x^3+5)^2

\int (x^{3} + 5)^{2} d x

\frac{x ^{7}}{7} + \frac{5 x ^{4}}{2} + 25 x + C

Solution steps

\int (x^{3} + 5)^{2} d x

Expand

(x^{3} + 5)^{2} : x^{6} + 10 x^{3} + 25

= \int x^{6} + 10 x^{3} + 25 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 x^{6} d x + \int 10 x^{3} d x + \int 25 d x

\int x^{6} d x = \frac{x ^{7}}{7}

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

\int 25 d x = 25 x

= \frac{x ^{7}}{7} + \frac{5 x ^{4}}{2} + 25 x

Add a constant to the solution

= \frac{x ^{7}}{7} + \frac{5 x ^{4}}{2} + 25 x + C

(x + 4)^{6} (x - 3)^{3}

cos (tan^{3} (x))

10 e^{- \frac{t}{2}}

\int cos (x) d (5 x) d x

{\frac{s}{s ^{2} + 2 s - 3}}

What is the integral of (x^3+5)^2 ?
The integral of (x^3+5)^2 is (x^7)/7+(5x^4)/2+25x+C