What is the integral of x4^{3x^2} ?

The integral of x4^{3x^2} is 2048x^2+C

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integral of x4^{3x^2}

\int x 4^{3 x^{2}} d x

2048 x^{2} + C

Solution steps

\int x \cdot 4^{3 x^{2}} d x

Apply u-substitution

: \int 2048 d u

= \int 2048 d u

Integral of a constant:

\int a d x = a x

= 2048 u

Substitute back

u = x^{2}

= 2048 x^{2}

Add a constant to the solution

= 2048 x^{2} + C

(x y + 2 x + y + 2) d x + (x^{2} + 2 x) d y = 0

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

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

2 x y y^{^{'}} = x^{2} + 2 y^{2}

f (x) = 2 e^{4 x}