What is the integral of 9x(4+3x)^5 ?

The integral of 9x(4+3x)^5 is 9(1/18 x(4+3x)^6-1/378 (4+3x)^7)+C

Popular >

integral of 9x(4+3x)^5

\int 9 x (4 + 3 x)^{5} d x

9 (\frac{1}{18} x (4 + 3 x)^{6} - \frac{1}{378} (4 + 3 x)^{7}) + C

Solution steps

\int 9 x (4 + 3 x)^{5} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int x (4 + 3 x)^{5} d x

Apply Integration By Parts

: \frac{1}{18} x (4 + 3 x)^{6} - \int \frac{1}{18} (4 + 3 x)^{6} d x

= 9 (\frac{1}{18} x (4 + 3 x)^{6} - \int \frac{1}{18} (4 + 3 x)^{6} d x)

\int \frac{1}{18} (4 + 3 x)^{6} d x = \frac{1}{378} (4 + 3 x)^{7}

= 9 (\frac{1}{18} x (4 + 3 x)^{6} - \frac{1}{378} (4 + 3 x)^{7})

Add a constant to the solution

= 9 (\frac{1}{18} x (4 + 3 x)^{6} - \frac{1}{378} (4 + 3 x)^{7}) + C

\int \frac{3 y ^{2}}{x - 5} d x

\int 0.1682 x^{2} + 0.0987 x + 0.4774 d x

\int x (3 x^{3} - 2) d x

\int \frac{tan ( x ) + cos ( x )}{sin ( 2 x )} d x

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

What is the integral of 9x(4+3x)^5 ?
The integral of 9x(4+3x)^5 is 9(1/18 x(4+3x)^6-1/378 (4+3x)^7)+C