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Popular >

integral of ba^x

Solution

\int b a^{x} d x

Solution

\frac{b a ^{x}}{ln ( a )} + C

Solution steps

\int b a^{x} d x

Take the constant out:

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

= b \cdot \int a^{x} d x

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

= b \frac{a ^{x}}{ln ( a )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{b a ^{x}}{ln ( a )}

Add a constant to the solution

= \frac{b a ^{x}}{ln ( a )} + C

Popular Examples

integral of (e^x-1/(7x))

\int (e^{x} - \frac{1}{7 x}) d x

integral of 1/8 e^{2x}

\int \frac{1}{8} e^{2 x} d x

integral of xln(2x^2+1)

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

integral of ((1+sin(x)))/(cos(x))

\int \frac{( 1 + sin ( x ) )}{cos ( x )} d x

integral of (x+3)/(x^2+5x+6)

\int \frac{x + 3}{x ^{2} + 5 x + 6} d x

Frequently Asked Questions (FAQ)

What is the integral of ba^x ?
The integral of ba^x is (ba^x)/(ln(a))+C