# Math Help - [SOLVED] integrals

1. ## [SOLVED] integrals

so we just learned integrals, and i'm having troubles solving this one:

dy/dx = (2e^x + sec(x)tan(x) - x^(1/2))

I've gotten to y= (2e^x)dx + sec(x) - (2/3)x^(3/2), but I can't figure out how to integrate 2e^x. please help?

2. Originally Posted by jahichuanna
so we just learned integrals, and i'm having troubles solving this one:

dy/dx = (2e^x + sec(x)tan(x) - x^(1/2))

I've gotten to y= (2e^x)dx + sec(x) - (2/3)x^(3/2), but I can't figure out how to integrate 2e^x. please help?
$\int e^x\,dx=e^x+C$...

3. I get that part, but where did the 2 come from?

4. Originally Posted by jahichuanna
I get that part, but where did the 2 come from?
The 2 appears in the original problem.

When you evaluate $\int 2e^x\,dx$, you can rewrite it by applying one of the integral properties. Its equivalent to $2\int e^x\,dx=2e^x+C$

Does this make sense?

5. ah, ok. thanks.

so the answer is 2e^x + sec x + (2/3)x^(3/2) + c?

6. Originally Posted by jahichuanna
ah, ok. thanks.

so the answer is 2e^x + sec x + (2/3)x^(3/2) + c?
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9672505259513855, "perplexity": 2820.0234167960493}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00284-ip-10-147-4-33.ec2.internal.warc.gz"}