What is the integral of (2x+5)4^{x^2+5x+1} ?

The integral of (2x+5)4^{x^2+5x+1} is (2^{2x^2+10x+1})/(ln(2))+C

Popular >

integral of (2x+5)4^{x^2+5x+1}

\int (2 x + 5) 4^{x^{2} + 5 x + 1} d x

\frac{2 ^{2 x^{2} + 10 x + 1}}{ln ( 2 )} + C

Solution steps

\int (2 x + 5) \cdot 4^{x^{2} + 5 x + 1} d x

Apply u-substitution

: \int 4^{u} d u

= \int 4^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{4 ^{u}}{ln ( 4 )}

Substitute back

u = x^{2} + 5 x + 1

= \frac{4 ^{x^{2} + 5 x + 1}}{ln ( 4 )}

Simplify

\frac{4 ^{x^{2} + 5 x + 1}}{ln ( 4 )} : \frac{2 ^{2 x^{2} + 10 x + 1}}{ln ( 2 )}

= \frac{2 ^{2 x^{2} + 10 x + 1}}{ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{2 x^{2} + 10 x + 1}}{ln ( 2 )} + C

\int \frac{4}{1 + ( x + 2 ) ^{2}} d x

\int \frac{cos ( y )}{sin ^{2} ( y ) + sin ( y ) - 2} d y

\int 250 (x + 4)^{3} d x

\int \frac{csc ^{4} ( x )}{cot ^{6} ( x )} d x

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

What is the integral of (2x+5)4^{x^2+5x+1} ?
The integral of (2x+5)4^{x^2+5x+1} is (2^{2x^2+10x+1})/(ln(2))+C