en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(x+8)^{15}

Solution

\int x (x + 8)^{15} d x

Solution

\frac{1}{2} x^{2} (x + 8)^{15} - \frac{1}{34} (15 x^{17} + 1785 x^{16} + 99008 x^{15} + 3394560 x^{14} + 80424960 x^{13} + 1394032640 x^{12} + 18249154560 x^{11} + 183534354432 x^{10} + 1427489423360 x^{9} + 8564936540160 x^{8} + 8^{10} \cdot 36465 x^{7} + 8^{11} \cdot 15470 x^{6} + 8^{12} \cdot 4641 x^{5} + 2^{38} \cdot 1785 x^{4} + 8^{14} \cdot 85 x^{3}) + C

Solution steps

\int x (x + 8)^{15} d x

Apply Integration By Parts

: \frac{1}{2} x^{2} (x + 8)^{15} - \int \frac{15}{2} x^{2} (x + 8)^{14} d x

= \frac{1}{2} x^{2} (x + 8)^{15} - \int \frac{15}{2} x^{2} (x + 8)^{14} d x

\int \frac{15}{2} x^{2} (x + 8)^{14} d x = \frac{1}{34} (15 x^{17} + 1785 x^{16} + 99008 x^{15} + 3394560 x^{14} + 80424960 x^{13} + 1394032640 x^{12} + 18249154560 x^{11} + 183534354432 x^{10} + 1427489423360 x^{9} + 8564936540160 x^{8} + 8^{10} \cdot 36465 x^{7} + 8^{11} \cdot 15470 x^{6} + 8^{12} \cdot 4641 x^{5} + 2^{38} \cdot 1785 x^{4} + 8^{14} \cdot 85 x^{3})

= \frac{1}{2} x^{2} (x + 8)^{15} - \frac{1}{34} (15 x^{17} + 1785 x^{16} + 99008 x^{15} + 3394560 x^{14} + 80424960 x^{13} + 1394032640 x^{12} + 18249154560 x^{11} + 183534354432 x^{10} + 1427489423360 x^{9} + 8564936540160 x^{8} + 8^{10} \cdot 36465 x^{7} + 8^{11} \cdot 15470 x^{6} + 8^{12} \cdot 4641 x^{5} + 2^{38} \cdot 1785 x^{4} + 8^{14} \cdot 85 x^{3})

Add a constant to the solution

= \frac{1}{2} x^{2} (x + 8)^{15} - \frac{1}{34} (15 x^{17} + 1785 x^{16} + 99008 x^{15} + 3394560 x^{14} + 80424960 x^{13} + 1394032640 x^{12} + 18249154560 x^{11} + 183534354432 x^{10} + 1427489423360 x^{9} + 8564936540160 x^{8} + 8^{10} \cdot 36465 x^{7} + 8^{11} \cdot 15470 x^{6} + 8^{12} \cdot 4641 x^{5} + 2^{38} \cdot 1785 x^{4} + 8^{14} \cdot 85 x^{3}) + C

Graph

Popular Examples

integral of y^{-1}+1/x

\int y^{- 1} + \frac{1}{x} d x

integral of (-x-3)/(x^2+1)

\int \frac{- x - 3}{x ^{2} + 1} d x

integral of 1/(12x^6)

\int \frac{1}{12 x ^{6}} d x

integral of ((sin(x))^3)/((cos(x))^4)

\int \frac{( sin ( x ) ) ^{3}}{( cos ( x ) ) ^{4}} d x

integral of 24x^3+34x+3

\int 24 x^{3} + 34 x + 3 d x

Frequently Asked Questions (FAQ)

What is the integral of x(x+8)^{15} ?
The integral of x(x+8)^{15} is