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

The integral of (x^2+3)^5 is (x^{11}}{11}+\frac{5x^9)/3+(90x^7)/7+54x^5+135x^3+243x+C

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integral of (x^2+3)^5

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

\frac{x ^{11}}{11} + \frac{5 x ^{9}}{3} + \frac{90 x ^{7}}{7} + 54 x^{5} + 135 x^{3} + 243 x + C

Solution steps

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

Expand

(x^{2} + 3)^{5} : x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 405 x^{2} + 243

= \int x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 405 x^{2} + 243 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^{10} d x + \int 15 x^{8} d x + \int 90 x^{6} d x + \int 270 x^{4} d x + \int 405 x^{2} d x + \int 243 d x

\int x^{10} d x = \frac{x ^{11}}{11}

\int 15 x^{8} d x = \frac{5 x ^{9}}{3}

\int 90 x^{6} d x = \frac{90 x ^{7}}{7}

\int 270 x^{4} d x = 54 x^{5}

\int 405 x^{2} d x = 135 x^{3}

\int 243 d x = 243 x

= \frac{x ^{11}}{11} + \frac{5 x ^{9}}{3} + \frac{90 x ^{7}}{7} + 54 x^{5} + 135 x^{3} + 243 x

Add a constant to the solution

= \frac{x ^{11}}{11} + \frac{5 x ^{9}}{3} + \frac{90 x ^{7}}{7} + 54 x^{5} + 135 x^{3} + 243 x + C

\int 42 sec^{4} (x) d x

x^{2}, 0, 2

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

\frac{d}{d x} (10 cos^{3} (x))

f (x) = sin (x) + \frac{3}{4} cot (x)

What is the integral of (x^2+3)^5 ?
The integral of (x^2+3)^5 is (x^{11}}{11}+\frac{5x^9)/3+(90x^7)/7+54x^5+135x^3+243x+C