What is the integral of (4x^2+5)^4 ?

The integral of (4x^2+5)^4 is (256x^9)/9+(1280x^7)/7+480x^5+(2000x^3)/3+625x+C

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integral of (4x^2+5)^4

integral

(4 x^{2} + 5)^{4}

\frac{256 x ^{9}}{9} + \frac{1280 x ^{7}}{7} + 480 x^{5} + \frac{2000 x ^{3}}{3} + 625 x + C

Solution steps

\int (4 x^{2} + 5)^{4} d x

Expand

(4 x^{2} + 5)^{4} : 256 x^{8} + 1280 x^{6} + 2400 x^{4} + 2000 x^{2} + 625

= \int 256 x^{8} + 1280 x^{6} + 2400 x^{4} + 2000 x^{2} + 625 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 256 x^{8} d x + \int 1280 x^{6} d x + \int 2400 x^{4} d x + \int 2000 x^{2} d x + \int 625 d x

\int 256 x^{8} d x = \frac{256 x ^{9}}{9}

\int 1280 x^{6} d x = \frac{1280 x ^{7}}{7}

\int 2400 x^{4} d x = 480 x^{5}

\int 2000 x^{2} d x = \frac{2000 x ^{3}}{3}

\int 625 d x = 625 x

= \frac{256 x ^{9}}{9} + \frac{1280 x ^{7}}{7} + 480 x^{5} + \frac{2000 x ^{3}}{3} + 625 x

Add a constant to the solution

= \frac{256 x ^{9}}{9} + \frac{1280 x ^{7}}{7} + 480 x^{5} + \frac{2000 x ^{3}}{3} + 625 x + C

(x + 1) sin (x^{2} + 2 x + 3)

x \cdot (x^{2} + 1)^{\frac{1}{2}}

ln (a^{2} - x^{2})

(x^{3} - 1)^{5}

\frac{x ^{2}}{x + 4}

What is the integral of (4x^2+5)^4 ?
The integral of (4x^2+5)^4 is (256x^9)/9+(1280x^7)/7+480x^5+(2000x^3)/3+625x+C