What is the integral of (x+1)3^{(x+1)^2} ?

The integral of (x+1)3^{(x+1)^2} is (3^{(x+1)^2})/(2ln(3))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+1)3^{(x+1)^2}

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

\frac{3 ^{(x + 1)^{2}}}{2 ln ( 3 )} + C

Solution steps

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

Apply u-substitution

: \int \frac{3 ^{u}}{2} d u

= \int \frac{3 ^{u}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int 3^{u} d u

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

= \frac{1}{2} \cdot \frac{3 ^{u}}{ln ( 3 )}

Substitute back

u = (x + 1)^{2}

= \frac{1}{2} \cdot \frac{3 ^{(x + 1)^{2}}}{ln ( 3 )}

Simplify

\frac{1}{2} \cdot \frac{3 ^{(x + 1)^{2}}}{ln ( 3 )} : \frac{3 ^{(x + 1)^{2}}}{2 ln ( 3 )}

= \frac{3 ^{(x + 1)^{2}}}{2 ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{(x + 1)^{2}}}{2 ln ( 3 )} + C

\int \frac{1}{x ( x ^{10} + 1 ) ^{2}} d x

\int (8 x^{2} + 7 x^{- 2}) d x

\int (3 x + 3)^{6} d x

\int 4 e^{x} + 3 d x

\int \frac{cos ( x )}{sec ^{5} ( x )} d x

What is the integral of (x+1)3^{(x+1)^2} ?
The integral of (x+1)3^{(x+1)^2} is (3^{(x+1)^2})/(2ln(3))+C