What is the integral of 10^{4t+1} ?

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

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integral of 10^{4t+1}

\int 1 0^{4 t + 1} d t

\frac{2 ^{4 t - 1} \cdot 5 ^{4 t + 1}}{ln ( 10 )} + C

Solution steps

\int 1 0^{4 t + 1} d t

Simplify

1 0^{4 t + 1} : 1 0^{4 t} \cdot 10

= \int 1 0^{4 t} \cdot 10 d t

Take the constant out:

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

= 10 \cdot \int 1 0^{4 t} d t

Simplify

1 0^{4 t} : 1000 0^{t}

= 10 \cdot \int 1000 0^{t} d t

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

= 10 \cdot \frac{1000 0 ^{t}}{ln ( 10000 )}

Simplify

10 \cdot \frac{1000 0 ^{t}}{ln ( 10000 )} : \frac{2 ^{4 t - 1} \cdot 5 ^{4 t + 1}}{ln ( 10 )}

= \frac{2 ^{4 t - 1} \cdot 5 ^{4 t + 1}}{ln ( 10 )}

Add a constant to the solution

= \frac{2 ^{4 t - 1} \cdot 5 ^{4 t + 1}}{ln ( 10 )} + C

\int \frac{( e ^{5 x} )}{7 + e ^{5 x}} d x

\int \frac{1}{5 + 5 x ^{2}} d x

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

\int e^{t a n (10 x)} sec^{2} (10 x) d x

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